According to a 115-count superseding indictment, appellants were major players in a sizable conspiracy to distribute drugs from 1983 to 1991 around the intersection of Lincoln Road and R Street in Northeast Washington, D.C.
The district court divided approximately twenty-four defendants into four groups for separate trials; the five appellants here comprise Group I. After a five-month trial and two weeks of jury deliberation, the jury on July 21, 1992 found all the appellants guilty of conspiring to distribute and possess with intent to distribute illegal drugs in violation of 21 U.S.C. § 846. Each appellant was also convicted of additional violations related to the drug conspiracy, including operating a *271continuing criminal enterprise (“CCE”) in violation of 21 U.S.C. § 848 (Kevin Williams-Davis, Anthony Nugent, and Darryl Williams); second-degree murder in violation of 22 D.C.Code § 2403 (Williams-Davis, Nu-gent, and Williams); violating the Travel Act, 18 U.S.C. § 1952(a)(3) (Alba Restrepo); and money laundering in violation of 18 U.S.C. § 1956 (Williams-Davis, Joyce Boyd). The jury acquitted appellants of violating the Racketeer Influenced and Corrupt Organizations Act (“RICO”), 18 U.S.C. § 1962(c).
Viewed in the light most favorable to the government, see United States v. Tarantino, 846 F.2d 1384, 1391 (D.C.Cir.1988), the evidence at trial established that Williams-Davis, Nugent, and Williams were the leaders of a large gang mostly made up of relatives and neighbors, the “R Street Crew.” Following the familiar pattern, see United States v. Childress, 58 F.3d 693, 711 (D.C.Cir.1995), these three used lieutenants who in turn paid others to sell drugs. The R Street Crew stored and packaged the drugs in sundry homes throughout the area. The gang would shift configuration slightly as various members were arrested and occasionally did time for drug offenses — including Nugent and Darryl Williams — but the basic structure held. In 1987 the group began selling cocaine, which Williams-Davis and Nugent obtained mostly from New York (a total of about 500 kilograms) and in part from California (about 150 kilograms). Defendant Alba Restrepo supplied cocaine to the group as its New York contact. Defendant Joyce Boyd helped Williams-Davis, her nephew, launder his hefty profits from the illegal drug sales. The group’s activities included bloody and sometimes deadly clashes with rival drug-peddling gangs. The R Street Crew came to the beginning of the end in 1990 after Jeffrey Williams (brother of Darryl) robbed a New York go-between, Claude Juggins, of his cocaine, prompting Juggins, caught between the R Street Crew and his Colombian suppliers (a rock and a hard place if ever there were), to turn FBI informant. The government was thereby able to tape and present to the jury telephone calls between Juggins and Williams-Davis, Nugent, and Restrepo.
Following trial, the district judge sentenced Kevin Williams-Davis, Anthony Nu-gent, and Darryl Williams to life imprisonment. He sentenced Joyce Boyd to 78 months’ imprisonment. On July 15,1992 the case was reassigned to another district judge who sentenced Alba Restrepo to 360 months’ imprisonment.
After the verdicts were returned, the district court evidently granted defense counsel permission to speak to such jurors as were willing. Appellants returned to court on September 21, 1992, filing a motion to dismiss or for a new trial based on affidavits from four jurors (a fifth juror affidavit was submitted a week later), claiming numerous instances of juror misconduct. On March 29, 1993, the court held a hearing to examine two of the alleged instances and issued an opinion denying the motions. United States v. Williams-Davis, 821 F.Supp. 727 (D.D.C. 1993). (We discuss these allegations in detail later.)
In this consolidated appeal, appellants make both collective and individual arguments. This opinion first discusses jury misconduct claims, common to all appellants. The next section describes additional arguments that most of the appellants join— including allegations of prosecutorial misconduct and the adequacy of the trial court’s jury instructions. The third section focuses on individual arguments. Specific facts are discussed as they become relevant. We have addressed the more deserving of appellants’ claims; the rest do not warrant treatment. We find none of appellants’ claims persuasive, except Nugent’s uncontested challenge to the second of his convictions under 18 U.S.C. § 924(c)(1), and so affirm appellants’ convictions on all counts but that one.
I. Jury Misconduct Issues
Appellants allege violations of their Sixth Amendment right to trial by an impartial jury and of their Fifth Amendment right to due process as a result of various forms of jury contamination and misconduct; independently they claim to be entitled to a new trial because of the trial court’s failure to conduct a more searching inquiry into these allegations. We discuss each of the alleged *272violations in turn. First, we address private contacts between jurors and third parties, including alleged comments by the forewoman’s husband and a telephone conversation between a juror and an alternate during deliberations. We then turn to juror exposure to more conventional sources of extrajudicial information, including media reports and use of a dictionary during deliberations. Finally, we examine a juror’s failure to disclose information during voir dire and predeliberation discussions among the jurors.
A. Private Communications With Jurors (Third Party Contacts)
There are two main assertions of illicit private communications to the jurors, one revolving around the forewoman’s husband, the other about an alternate who communicated with one of the jurors after having been dismissed for the deliberations. Four jurors gave affidavits after trial saying that the forewoman said that her husband told her to “nail” the defendants. One alternate juror supplied dim support, saying that the forewoman talked “a lot” about what her husband thought of the case, but that she could not remember specific comments. She also claimed that the husband came to court frequently, maybe three or four times a week. The district court held a hearing to question the forewoman, who stated that she had discussed the evidence once with her husband during the trial but that he had not commented, and that he had come to see the trial on two occasions. The court credited the forewoman’s statement that her husband didn’t say anything about defendants’ guilt, and noted the tensions that had existed among some of the jurors because of the forewoman’s strong personality. 821 F.Supp. at 746-47. The court did not call the jurors who had given affidavits, concluding that even if the forewoman had relayed the alleged remark, it would not have been adequate to support a finding of actual prejudice.
The second claim arises from the post-trial affidavit of alternate juror Shalita Isaac, who was dismissed before deliberations began, saying that juror Carl Biggs called her during deliberations and said that he was trying to tell the marshal he needed to talk to the judge about the forewoman. Isaac claimed that Biggs said the forewoman “wanted RICO badly,” and that Isaac told Biggs not to take Nugent’s houses and cars in forfeiture because Nugent had children who needed them. According to Isaac, Biggs said “he was going to do the best he could.” In other words, by her own account the dismissed alternate weighed in on the side of the defendants on the only merits issue as to which she expressed an opinion.
We start with the obviously more serious episode, the forewoman’s husband’s supposed exhortation to “nail” the defendants. Here appellants argue first that prejudice must be presumed, and second that the judge should have held a more extensive hearing.
The claim of presumption rests largely on Remmer v. United States, 347 U.S. 227, 74 S.Ct. 450, 98 L.Ed. 654 (1954), where the Court spoke of a presumption of prejudice from private contacts with the jurors: “In a criminal case, any private communication, contact, or tampering, directly or indirectly, with a juror during a trial about the matter pending before the jury is ... deemed presumptively prejudicial____” Id. at 229, 74 S.Ct. at 451. The court stated that “[t]he presumption is not conclusive, but the burden rests heavily on the Government to establish, after notice to and hearing of the defendant, that such contact with the juror was harmless to the defendant.” In Remmer, a juror reported an attempt to bribe him to the judge, who then requested an FBI investigation. An FBI report concluded that the contact was made in jest, and the court consulted with the prosecutors, who agreed the contact was harmless. The Supreme Court seemed particularly concerned that the defense had no inkling of what had happened; hence the emphasis on notice to the defendant and a hearing: “The trial court should not decide and take final action ex parte on information such as was received in this case, but should determine the circumstances, the impact thereof upon the juror, and whether or not it was prejudicial, in a hearing with all interested parties permitted to participate.” Id. at 229-230, 74 S.Ct. at 451.
*273Remmer preceded adoption of Rule 606(b) of the Federal Rules of Evidence, which interestingly cut off the principal means by which one might directly dispel the presumption of prejudice — interrogation of jurors as to the impact of an improper contact:
Upon an inquiry into the validity of a verdict or indictment, a juror may not testify as to any matter or statement occurring during the course of the jury’s deliberations or to the effect of anything upon that or any other juror’s mind or emotions as influencing the juror to assent to or dissent from the verdict or indictment or concerning the juror’s mental processes in connection therewith, except that a juror may testify on the questions whether extraneous prejudicial information was improperly brought to the jury’s attention or whether any outside influence was improperly brought to bear upon any juror.
(Emphasis added.) The exception for improper outside influence allows testimony about the fact and nature of the contact (the input, as it were), but not about the effect it produced on the juror’s state of mind. See Tanner v. United States, 483 U.S. 107, 116-27, 107 S.Ct. 2739, 2745-51, 97 L.Ed.2d 90 (1987) (explaining the origins of and rationale behind the rule); United States v. Maree, 934 F.2d 196, 201 (9th Cir.1991) (distinguishing between statement and its impact). Thus, if the Remmer presumption applied in full force, Rule 606(b) would generally make it difficult or impossible to overcome a presumption of prejudice once a jury had reached its verdict and a third-party contact were shown. The Tenth Circuit has suggested, accordingly, that “[t]his effect of Rule 606(b) may require the courts to narrow [Remmer’s] definition of ‘presumptively prejudicial.’ ” United States v. Greer, 620 F.2d 1383, 1385 n. 1 (10th Cir.1980).
And narrow they have. In Smith v. Phillips, 455 U.S. 209, 102 S.Ct. 940, 71 L.Ed.2d 78 (1982), a habeas case, the Court addressed a claim of juror partiality based on the juror’s having applied for a job with the prosecutor’s office. Overturning the lower federal courts’ insistence on a new trial, the Court said, “This Court has long held that the remedy for allegations of juror partiality is a hearing in which the defendant has the opportunity to prove actual bias.” 455 U.S. at 215, 102 S.Ct. at 945 (emphasis added). Of course one might distinguish between juror partiality and private contacts, but, far from doing so, the Court cited Remmer, and the attempted juror bribe there, as an illustration of the principle it was invoking. But assuring the defendant “an opportunity to prove actual bias” is out of synch with the Remmer presumption; why would a defendant enjoying a presumption in his favor need such an opportunity? Accordingly, the court in United States v. Pennell, 737 F.2d 521, 532-33 (6th Cir.1984), explicitly construed Phillips as working a substantive change in the law, eliminating any presumption of prejudice and placing on defendant a burden of showing prejudice.
The Supreme Court also seemed to reconfigure Remmer in United States v. Olano, 507 U.S. 725, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993) (applying the plain error standard). There, with the acquiescence of counsel, alternate jurors sat with the jury during deliberations but were told by the trial court not to participate. In its discussion of what it called “intrusion” jurisprudence (outside intrusions on the jury), the Court appeared to see Remmer largely as a case illustrating the importance of weighing the likelihood of prejudice rather than as a source of rigid rules.
There may be cases where an intrusion should be presumed prejudicial, ... but a presumption of prejudice as opposed to a specific analysis does not change the ultimate inquiry: Did the intrusion affect the jury’s deliberations and thereby its verdict? We cannot imagine why egregious comments by a bailiff to a juror {Parker) or an apparent bribe followed by an official investigation (Remmer) should be evaluated in terms of “prejudice,” while the mere presence of alternate jurors during juror deliberations should not.
Id. at 739, 113 S.Ct. at 1780-81 (emphasis partially added).
Although often referring to Remmer, this court has in fact not treated the supposed “presumption” as particularly forceful, but rather has accepted the necessity of focusing *274on the specific facts of the alleged contact, and, as a result, has found broad discretion in the trial court to assess the effect of alleged intrusions. In United States v. Williams, 822 F.2d 1174, 1188 (D.C.Cir.1987), a defense witness told three jurors at the end of the first day’s deliberations that they were deliberating so long only to collect more jurors’ fees. Noting that assessment of the bias required consideration of a range of factors, including “the nature of the communication, the length of the contact, the possibility of removing juror taint by a limiting instruction, and the impact of the communication on both the juror involved and the rest of the jury,” id. at 1188-89, we said that the trial judge was best qualified to make the assessment, so that its “rulings on a motion for a mistrial [for juror bias] will be overturned only for an abuse of discretion,” id. at 1188. See also United States v. Fafowora, 865 F.2d 360, 363 (D.C.Cir.1989) (stressing deference to district court’s assessment of effect of third-party communications); United States v. Butler, 822 F.2d 1191, 1196 (D.C.Cir.1987) (same).
Thus we think the district court was correct under the Supreme Court’s and our cases to inquire whether any particular intrusion showed enough of a “likelihood of prejudice” to justify assigning the government a burden of proving harmlessness. See 821 F.Supp. at 738 (applying the analysis to exposure to newspaper articles). (In the ease of the forewoman’s husband’s alleged remarks, the district court appeared to apply the same analysis as an alternative basis for its holding. Id. at 747.) We understand the court’s decision in Stockton v. Commonwealth of Virginia, 852 F.2d 740 (4th Cir. 1988), saying that “while a presumption of prejudice attaches to an impermissible communication, the presumption is not one to be casually invoked;” id. at 745, as effectively embracing that view.
As we said, the court credited the forewoman but, assuming in the alternative that the remark had been made, concluded that it would not have been prejudicial. Appellants say this was error, and cite several eases from other circuits to support their position. Thus the court remanded for a new trial in Maree, where a juror consulted with two friends who told her “people like [defendant] should be incarcerated,” 934 F.2d at 202; in Greer, where the jurors had chatted with a marshal about the defendant’s possible sentencing (and expungement of conviction) under the Youth Corrections Act, 620 F.2d at 1385; and in Stockton, where the owner of a diner at which the jurors were lunching during deliberations told jurors “they ought to fry the son of a bitch,” 852 F.2d at 743-44.
Whether we focus on the forewoman herself or the other jurors, however, we think the district court was within its discretion in concluding that the remark was not likely to have had any effect on the outcome. Although the supposed remark was forceful, it was isolated; the fifth juror’s claim that more than one of the husband’s opinions had been relayed was supported by no other jurors and contained no specifics. Further, the judge, who was in a position to observe and whose comment defendants do not contradict, said the forewoman had a “strong personality,” and had “leaned heavily toward conviction during deliberations,” 821 F.Supp. at 746, suggesting the improbability that the supposed remark either could have affected her own views or could have added much to any influence she may have had on fellow jurors. Thus, still indulging the assumption that the remark was made at all, the husband’s two cents’ worth appears subordinate in a way that could not possibly be said of the third-party comments that intruded in the cases relied on by appellants, which in any event display less deference to the district court than does this circuit and which in some eases seem to apply a strong presumption of prejudice to all or at least a very broad set of third-party contacts.
Moreover, the evidence against defendants was overwhelming. Cf., e.g., Dallago v. United States, 427 F.2d 546, 558 (D.C.Cir. 1969) (reversal because of presence of unadmitted document in jury room would not be appropriate where other proof of guilt was “overwhelming”: “Certainly the weight of the prosecution’s evidence becomes relevant in estimating “what effect the error had or reasonably may be taken to have had upon the jury’s decision.’”) (quoting Sawyer v. *275United, States, 303 F.2d 392, 395 (D.C.Cir. 1962)); United States v. Smith, 85 F.3d 646, 646 (D.C.Cir.1996) (denying petition for rehearing). Here, the FBI recorded most of the 1990 conversations between defendants Williams-Davis and Nugent and their New York suppliers, defendant Restrepo and Jimmy Bynoe, through the go-between Claude Juggins. In these conversations, defendants worked out deals to buy (and sell, in the case of Restrepo) large amounts of cocaine. Williams-Davis and Nugent showed themselves to be familiar with the prices of such amounts and confident of their ability to move them. In November 1990, for example, in the midst of discussions about a new deal, Nugent told Juggins that it would take him only a week to sell ten kilograms of cocaine. This confidence was well-founded; searches of R Street Crew stash houses revealed an elaborate apparatus for distributing cocaine (as well as large amounts of drugs and cash). The various houses and apartments contained a heat sealer and extensive packaging materials, money counters, electric scales, guns, and bullet-proof vests.
Testimony showed that Williams-Davis, Nugent, and Darryl Williams were leaders of the Crew, supervising a wide array of lieutenants, second lieutenants, runners, packagers, stash house owners, and others. They enforced the Crew’s control over the neighborhood with violence, deadly if need be. On April 3, 1985, an argument broke out between Leon Clea — a leader of a rival drug gang — and Williams-Davis, Nugent, Darryl Williams, and other R Street Crew members over the gangs’ competing territorial claims. R Street Crew members armed themselves and started shooting. According to Kenneth Watts (a cousin of Clea’s) and Leon Clea himself, Darryl Williams shot Alton Clea (brother of Leon) point-blank in the face, killing him. Leon Clea further testified that Sean Martin, an R Street Crew lieutenant and brother of Anthony Nugent, shot Leon’s brother Andre Clea in the foot, and that Nugent shot and wounded Leon himself. Those accounts mesh with that of Tracy Cave, an R Street Crew member, and a police sergeant who arrived on the scene shortly after the shootings. During a territorial dispute with the Bailey clan (to which we return later), Nugent and Kevin Williams-Davis together with other Crew members went to the Baileys’ car repair shop seeking revenge for the killing of Nugent’s brother. During the fray, Freddie Bailey was hit about 10 times but somehow managed to survive. Francis Scrivener, who was in the shop, was not so lucky: he was shot once and died.
Dale Webster, a coeonspirator but one who provided very detailed descriptions, many of which were confirmed by other evidence, testified that defendant Joyce Boyd — who is Kevin Williams-Davis’s and Darryl Williams’s aunt — joined the conspiracy early. In late 1984 or early 1985, Webster said, Boyd recruited Webster to operate a stash house for her nephews. One day in early 1985, when Boyd and Webster were in Webster's house together, police showed up outside and the two flushed several thousand dollars’ worth of cocaine down the toilet. Webster, with Boyd present, later explained to Williams-Davis what had happened. R Street Crew member Kenneth Sparrow’s testimony confirmed Webster’s. He said, for example, that at one point Jeffrey Williams had told him to take a day’s proceeds (about $1,500 in cash) to “Joyce” at the Ebony Connection (her beauty shop), which he did. On the money laundering counts (which of course also involve conscious assistance to the drug conspiracy), the government showed through bank records that Boyd paid over $85,000 to lease and eventually buy a Mercedes that Williams-Davis was arrested driving in December 1988. The title was in Boyd’s name only, and Williams-Davis’s name does not appear on any of the financing documents. In June 1991 a search of Boyd’s apartment turned up a 1990 proof of insurance form for the Mercedes in the names of both Williams-Davis and Boyd.
It is possible — and appellants appear to argue — that the court erred in confining the hearing as it did, quite independently of its alternative ruling that the alleged statement would not have been prejudicial. But our eases say clearly that the trial court has broad discretion over the “methodology” of inquiries into third-party contacts with jurors. Williams, 822 *276F.2d at 1190. We have explicitly rejected any automatic ride that jurors are to be individually questioned. Id. at 1190 n. 162. This latitude explicitly covers trial courts’ choices as to the proper procedures for post-trial hearings. United States v. Butler, 822 F.2d 1191, 1196 (D.C.Cir.1987). The “inquiries put to the juror need only be sufficiently detailed to permit the judge to determine whether any prejudice is likely to result.” Id. Further, we think the court could properly consider, among the factors militating against extending the inquiry, the risk that massive examination and cross-examination would in fact amount to “juror harassment.” See 821 F.Supp. at 735; Tanner, 483 U.S. at 119-20, 107 S.Ct. at 2746-48 (addressing asserted juror alcohol and drug use, Court observed that if juror affidavits were readily accepted to overturn verdicts, “‘[jjurors would be harassed and beset by the defeated party in an effort to secure from them evidence of facts which might establish misconduct sufficient to set aside a verdict’”) (quoting McDonald v. Pless, 238 U.S. 264, 267-68, 35 S.Ct. 783, 784-85, 59 L.Ed. 1300 (1915)). In any event, we think that where the court conducts an inquiry broad enough to lead it to a reasonable judgment that there has been no prejudice, on an assumption as to the facts favorable to defendants’ claim, it has fulfilled its procedural as well as its substantive duty.
The telephone call from Isaac, the dismissed alternate juror, to Biggs, illustrates the importance of a non-literalist interpretation of Remmer. Though appellants characterize it as an alternate juror’s “participation in deliberations,” and say that the trial court erred in failing to conduct a hearing, the colloquy was trivial on its face. According to Isaac’s own affidavit her comments were favorable to defendants. While we can imagine such an intervention having a boomerang effect, that was plainly not true here. The jury acquitted defendants on the RICO counts, and, because the trial court dismissed the government’s forfeiture case involving Nugent’s house, the jury never addressed that issue. While the jury decided in favor of the forfeiture of Nugent’s Mercedes, contrary to Isaac’s alleged advice, it seems a great stretch to view that rather trivial aspect of the outcome to a boomerang effect from the phone call. As even appellants grudgingly admit, “On a superficial level, perhaps, one could say that this particular ex parte contact did not prejudice Appellants.” There is no reason to think that the result is otherwise at a non-superficial level.
B. Juror Exposure to Extra-judicial Information
1. Juror Exposure to Media Reports
In the course of the trial two articles appeared in the Washington Post that led the court to conduct voir dires of the jurors to make sure there had been and would be no prejudice. While appellants do not claim error in the trial court’s contemporaneous handling of these episodes, they object to the court’s failure to recall the jurors when several of them signed post-trial affidavits asserting that there had been more exposure to the papers — particularly to these articles— than the jurors had acknowledged in the voir dires. But the material to which the jurors belatedly claimed exposure was in its essence cumulative of trial evidence. We find no error.
On March 13, 1992, about a month after the jury was sworn, the Post ran a front-page article, Michael York, ‘Witness Threats Reported In R Street Drug Trial,” saying that two government witnesses had been threatened and that signs had been posted in the R Street area warning “snitchers.” That morning defendants moved for a mistrial and the court, after verifying that there were no newspapers in the jury room, conducted an individual voir dire of each juror. Two jurors said they had heard “a report” about threats to witnesses, 821 F.Supp. at 736, but both said the report would not affect their ability to be impartial. All jurors said they would avoid press reports and would base their verdict solely upon the evidence at trial. Id. at 735-36. On May 18,1992 the Post ran another front-page story called “Enforcers Are D.C.’s Dealers of Death” (by Pierre Thomas and Michael York), which mentioned Nugent by name as an example of an enforc*277er who maintained a drug gang’s control over territory. Again the trial court conducted individual voir dire of the jurors, and all disclaimed familiarity with the article. 821 F.Supp. at 736.
After the trial, four jurors gave affidavits stating that other jurors read newspaper accounts of the trial and discussed them in the jury room. Interestingly, only one of these affiants participated in the final verdict, as two were alternates and one was dismissed midway through the deliberations. (Dews and Isaac, and Scott, respectively.) A fifth juror, Garnett, uniquely admitted reading an article himself, saying that he had seen, and had falsely denied seeing, the article on death threats to witness, presumably referring to the March 13, 1992 article. He also said the jurors had read articles that the judge did not inquire about, citing “the one where the government was saying they had to use different means to get witnesses to cooperate.” (An article submitted in post-trial proceedings matching this description is Michael York & Sari Horwitz, “Threats to Witnesses Increasing in District,” Wash. Post, Mar. 16, 1992, at Dl, mentioning problems with persuading witnesses to testify for the government in the R Street trial.) And Garnett claimed that “[w]e also heard about the case on the radio and TV.”
The trial court ruled that the affidavits would warrant a hearing only if they showed a likelihood of prejudice, 821 F.Supp. at 738, and concluded that they did not. Although finding the jurors’ responses on voir dire more credible than their recantations, id. at 736, the court also found that “neither [of the two articles occasioning a voir dire] contained extraneous, extra-judicial information about defendants that could have prejudiced their right to a fair trial.” Id. at 737. In particular, the court detailed government evidence at trial for the murders of rival drug dealers mentioned in the May 18 article. Id. The court’s approach here, inquiring into whether the alleged improper exposures were cumulative, fully accords with our treatment of other types of exposures to extra-judicial material. See, e.g., Dallago, 427 F.2d at 559 (delivery into jury room of unadmitted document is harmless error where it was merely cumulative of properly admitted evidence); United States v. Treadwell, 760 F.2d 327, 339 (D.C.Cir.1985) (similar). The court found that “[w]hat little extra-judicial information each article did contain about defendants was merely duplicative of evidence already introduced in open court____” 821 F.Supp. at 738.
Appellants do not contest that finding except as to the Post articles alluding to threats to witnesses. While the government argues that this was cumulative because the witness Rosalind Cherry revealed these threats to the jury, appellants correctly point out that she denied ever being threatened by defendants. The record, nonetheless, shows that Cherry intensely feared retaliation; given her familiarity with defendants, one would have to be quite obtuse not to suppose that the fear derived from that familiarity. She admitted that she was “scared” to testify, that the government had recently given her money to move out of Southeast Washington, and that three or four agents surrounded her when she went to court to testify. Given this information, coupled with the defendants’ practice of removing or attempting to remove other people who proved inconvenient, which was amply shown at trial, the material in the article appears largely cumulative.
There are, in addition, juror Garnett’s allegations of exposure to other sources, such as radio and television reports. But Gar-nett offered no detail from which one could infer that this added anything to the trial evidence itself. Further, the court found Garnett’s affidavit to be particularly suspect because of a likely motive to impeach his verdict. 821 F.Supp. at 755. Garnett was quoted in a post-trial Post article, Michael York & Linda Wheeler, “Fear Said to Affect R St. Jury,” July 24, 1992, at Bl, saying that he was surprised to learn that three defendants would receive life without parole despite acquittal on the RICO charges. He said he had focused on the racketeering charges, knew that this was the first time prosecutors had attempted to get convictions for a local drug gang using RICO, and expressed his disapproval of the effort. The U.S. Attorney’s office had brought the charges, he said, “‘to satisfy the public,’” *278and he was “ ‘disturbed’ ” that “the government appeared more concerned with prosecuting the R Street defendants than their cocaine suppliers in Central America.” Id. Given Garnett’s self-description as a person who entered the jury room with an agenda of limiting the damage to defendants, we think the district court was well within its discretion in declining to summon the jurors back.
On these media exposures we note again the overwhelming character of the evidence against defendants, making the chance that these exposures could have affected the verdict exceedingly remote. See pages 274-75 above.
We note, finally, that the one shred of evidence as to whether the jurors allowed the press to influence them suggests that they did not. Isaac’s affidavit refers to an April 23, 1992 Post article that mentioned the purchase of a pair of custom-made baby alligator shoes costing about $2,200, apparently for. Williams-Davis. Michael York, “R Street Crew Leaders Were Big Spenders,” Wash. Post, Apr. 23,1992, at C3. Isaac says of the article, “Once there was a mistake in the paper about the $2,000 shoes.” The comment indicates that Isaac, quite properly, trusted her own recollection of the evidence over the Post reporter’s. Cf. 821 F.Supp! at 741 (observing that the matters in the article were merely duplicative of trial evidence).
In affirming the trial court, we endorse its view that defendants bringing post-trial claims of mid-trial media exposure must make a threshold showing of a likelihood of prejudice. We reach this conclusion quite independently of our earlier conclusion that the presumption of prejudice stated in Remmer’a initial formulation has. eroded; we think Remmer never applied at all outside the area of private contacts with jurors.
The few decisions in the courts of appeals that explicitly address juror exposure to mid-trial publicity have not applied the Remmer presumption. See, e.g., Waldorf v. Shuta, 3 F.3d 705, 710 (3d Cir.1993) (stating that defendants have burden of showing likelihood of actual prejudice); United States v. Boylan, 898 F.2d 230, 258-60 (1st Cir.1990). In Boylan the court confined Remmer on the grounds that the media exposure lacked the characteristics stressed by the Remmer Court as justifying the presumption, namely, the paucity of data about the event (an attempted bribe) and its extreme nature. Boylan specifically notes that “the absence of third party involvement” makes it much easier to secure a picture of what has happened, id. at 260; that absence is, of course, typical of media exposure episodes. Cf. United States v. Herring, 568 F.2d 1099, 1103 (5th Cir.1978) (“presumption” of prejudice nominally applied, but with court finding specific timing and content of article highly prejudicial); United States v. Manzella, 782 F.2d 533, 542 (5th Cir.1986) (no prejudice although jurors read article telling of defendant’s prior conviction, where in mid-trial voir dire they said that they had noticed only facts brought out at trial). Indeed, on its face Remmer refers only to a “private communication, contact, or tampering” with a juror. 347 U.S. at 229, 74 S.Ct. at 451. We agree that not even a diluted version of the Remmer presumption applies in cases of juror exposure to media coverage about the case (except perhaps in an instance where someone was deliberately using the media to contact the jurors). But see United States v. Posner, 644 F.Supp. 885, 887 (S.D.Fla.1986) (applying Remmer presumption to case of mid-trial juror media exposure; reversing conviction), aff'd. sub nom. United States v. Scharrer, 828 F.2d 773 (11th Cir.1987) (table).
The Third Circuit in Waldorf v. Shuta set forth an approach for mid-trial claims of media exposure that seems to us a basis, with suitable adjustments, for post-trial claims. That decision directed district courts to (1) determine if material is prejudicial; (2) determine whether jurors were exposed to it; and (3) examine exposed jurors to determine if their impartiality was compromised, 3 F.3d at 709-10, and it assigned defendants the burden of showing the likelihood of actual prejudice, id. Where the issue is raised post-trial, of course, F.R.E. 606(b) forbids examining jurors directly on their impartiality (the third step), and because they have dispersed it is far more burdensome to query them even on the aspect permitted by-Rule 606(b) — the degree of *279exposure (the second step). Accordingly, then, the court should address the first step (as it did here), taking into account the degree to which the material was cumulative and whether the evidence against defendants was (as here) overwhelming. If prejudice is likely, then inquiries as to the degree of exposure are necessary, and, ultimately, some judgment as to the likely impact on impartiality. Our review of the district court findings is deferential, as it is for review of trial court handling of pre-trial publicity, Childress, 58 F.3d at 706 (trial court’s finding of juror impartiality only reviewed for “manifest error”), and of private communications to jurors, see pages 273-74 above. As our analysis above makes clear, in applying these standards we find no error in the scope of the district court’s inquiry and its finding of no prejudice from the almost entirely cumulative material.
2. Jurors’ Use of a Dictionary
In their affidavits, two jurors stated that during deliberations the forewoman looked up the word “enterprise” in a dictionary and read out the definition to persuade jurors to convict. According to juror Scott, the forewoman was trying to persuade fellow jurors on the continuing criminal enterprise count. The district court found this use of a dictionary to be not prejudicial because the term “enterprise” was legally significant only for the EICO counts, see 18 U.S.C. §§ 1961(4), 1962, and the jury acquitted defendants of these charges. As to the CCE counts, the statute uses the term “enterprise” only in labelling the crime, not in identifying any of the criteria that must be satisfied to show the crime’s commission. 21 U.S.C. § 848(c). The court therefore decided that “jury consideration of a dictionary definition of that word does not implicate the dangers usually associated with this form of juror misconduct.” 821 F.Supp. at 739. Appellants contend that because the jury could have looked up other words in the dictionary, and because the use of a dictionary definition of “enterprise” could have been prejudicial on the CCE counts despite its irrelevance to the necessary jury findings, the trial court should have recalled the jury for questioning.
Again we see no reason why a presumption of prejudice should be suitable for this sort of extraneous material, any more than it would be for media exposure. Cases from other circuits are mixed. The Eighth Circuit has declined to apply a Remmer presumption to jurors’ use of extraneous material for resolution of a legal as opposed to a factual issue, United States v. Blumeyer, 62 F.3d 1013, 1016-17 (8th Cir.1995), a distinction that the court does not explain and that does not on its face seem convincing. The Sixth Circuit has applied concepts in accord with our general treatment of extraneous materials, saying that prejudice is not to be automatically inferred even if jurors in fact studied a dictionary definition. United States v. Gillespie, 61 F.3d 457, 460 (6th Cir.1995). On that court’s view the trial court has extensive discretion to fashion its inquiry, and review is for abuse of discretion. Id. See also United States v. Duncan, 598 F.2d 839, 866 (4th Cir.1979) (same). While United States v. Martinez, 14 F.3d 543, 550 (11th Cir.1994), applied a Remmer presumption to jurors’ use of a dictionary, the case involved intrusion of many other extraneous materials, which the court in fact found prejudicial. And in a civil case the Tenth Circuit spoke of its application of Remmer to any “external information,” but in fact the court delineated a range of factors to be considered in estimating the likelihood of prejudice. Mayhue v. St. Francis Hospital, 969 F.2d 919, 922-23 (10th Cir.1992). Cf. United States v. Console, 13 F.3d 641, 665-66 (3d Cir.1993) (purporting to apply Remmer presumption to erroneous definition originating in juror’s sister). Obviously where the word is critical to a necessary determination, a finding of prejudice is likely. See, e.g., Marino v. Vasquez, 812 F.2d 499, 505-06 (9th Cir.1987) (presence of “malice,” which jurors looked up in the dictionary after thirty days’ deliberation, was crucial to conviction); Mayhue, 969 F.2d at 924.
We see no need for further proliferation of categories, and think the alleged contamination is properly assessed in accordance with the standards outlined above for post-trial claims of media exposure—the burden is on defendant to show prejudice, which at the *280outset is to be done by examination of the alleged illicit exposure in the full context of the trial. Here the defendants have not gotten past the first step. They have not shown that the portion of the dictionary to which the jurors were exposed eould, in its nature, have played a prejudicial role. The word looked up had no legal relevance to the findings necessary for the charges on which the jury convicted, and the defendants, despite their counsel’s access to quite a few evidently regretful jurors, offer no reason to believe that the jury looked up other words.
C. Juror’s Failure to Disclose Information During Voir Dire
Alternate juror Isaac’s affidavit claimed that juror Biggs used to live on R Street and “could place [Williams-Davis’s and Nugent’s] faces from growing up on R Street.” At the initial voir dire jurors were asked whether they were familiar with the R Street and Lincoln Road neighborhood, and Biggs had not responded. At a post-trial hearing the court questioned Biggs, who said that he had lived in Washington for 13 years, and that he had lived at 1630 Lincoln Road for four months when he first moved to the area in June 1980. He had then moved to Florida Avenue and had not been back to the R Street neighborhood since. He said he had never seen defendants before the trial. When asked why he had not responded at voir dire, he said (without further elaboration) that he had not thought it was necessary. 821 F.Supp. at 748-49. The court credited his testimony and concluded that Biggs had been making a sincere effort to respond truthfully and was not biased against defendants, noting that “[h]is sojourn in that neighborhood was brief and ended well before any of the criminal activities at issue in this trial occurred.” Id. at 749. Appellants argue that a new trial is needed because of “Biggs’ knowledge of the R Street neighborhood and drug dealers whose names frequently surfaced at trial, such as Rayful Edmond, III” — the last item evidently referring simply to Biggs’s knowledge of the name Rayful Edmond, a much-publicized District drug dealer.
For reversal because of a juror’s failure to disclose information at voir dire, the Supreme Court requires the complaining party to show that the juror “failed to answer honestly a material question on voir dire, and then further show that a correct response would have provided a valid basis for a challenge for cause. The motives for concealing information may vary, but only those reasons that affect a juror’s impartiality can truly be said to affect the fairness of a trial.” McDonough Power Equip., Inc. v. Greenwood, 464 U.S. 548, 556, 104 S.Ct. 845, 850, 78 L.Ed.2d 663 (1984). We applied the McDonough standard in United States v. North, 910 F.2d 843, 903-04 (D.C.Cir.1990), reading it to require a showing of actual bias, id. at 904. We upheld the trial court’s finding that there was no actual bias, even though the trial court disbelieved the juror’s post-trial “forgetfulness” explanation of her failure to reveal that several of her brothers had been charged with criminal conduct, that one had been sent to prison, and that she herself had testified before a grand jury investigating a robbery allegedly committed by one of her brothers. We review the trial court’s decision for abuse of discretion. United States v. Boney, 68 F.3d 497, 502 (D.C.Cir.1995).
Plainly the omission here does not remotely satisfy the daunting McDonough-North standard. Apart from the comparative triviality of the omission, the only specific indications about Biggs suggest that he was favorably disposed to the defendants, as he had told Isaac, according to her report of her mid-deliberations phone conversation with him, that “he was going to do the best he could” to carry out her plea to prevent the forfeiture of Nugent’s houses and ears. And juror Scott stated that Biggs, Scott himself, and several other jurors “were all in agreement that we needed to have all of the evidence and take our time deliberating without being coerced to just find them guilty.”
There is a loose end here. Isaac’s claim that Biggs “could place [Williams-Davis’s and Nugent’s] faces from growing up on R Street” was based, she said, on a drive the two took together around the R Street neighborhood because she (Isaac) “didn’t know where it was at.” She said Biggs *281pointed out where various members of the R Street Crew used to live. The trial court questioned Biggs about the trip after the trial and concluded that the drive could not possibly have been prejudicial because, during trial, the jurors had repeatedly viewed enlargements of aerial photographs and street photographs of the R Street neighborhood. 821 F.Supp. at 741. Thus the information gained from the illicit drive appears to be entirely cumulative. Cf. Bibbins v. Dalsheim, 21 F.3d 13, 17 (2d Cir.1994) (in light of introduction of crime scene photographs at trial, relaying of extra-record information by juror familiar with the crime scene was cumulative). Defendants do not claim that Biggs actually knew any defendant, or that more inquiry was needed on that red herring.
D. Pre-deliberation Discussions
The five juror affiants all indicated that jurors discussed the case before deliberations. Because the only “extraneous” material shown as having been discussed was the article restating the alligator shoes testimony, see page 278 above, the court held that the jurors’ statements about the conversations were inadmissible under Rule 606(b). 821 F.Supp. at 741 — 42.
Appellants argue that Rule 606(b) does not apply to pre-deliberation discussions, since the Rule on its face applies only to deliberations. Accordingly, they say, the court should have questioned the entire jury on this point. The government counters that Rule 606(b) does not apply to pre-deliberation discussions discovered mid-trial, but does apply to the same discussions discovered post-trial.
While the law is slightly obscure, it appears that even if Rule 606(b) does not actually bar receipt of evidence of pre-deliberation discussions, a trial court is virtually automatically justified in declining to pursue such an inquiry. In Tanner v. United States, 483 U.S. 107, 107 S.Ct. 2739, 97 L.Ed.2d 90 (1987), the Court considered post-trial claims that members of the jury had, during the trial, consumed so much alcohol at lunch that they had slept through afternoon sessions of the trial. The Court read Rule 606(b) as drawing a distinction between external influences (admissible under the exception) and “internal” matters, among which the common law had firmly classified the jurors’ physical or mental incompetence. Id. at 117-18, 107 S.Ct. at 2745-46. The trial judge had refused to pursue the defendants’ allegations of drinking and sleeping, and the Supreme Court said that it “did not err in deciding, based on the inadmissibility of juror testimony and the clear insufficiency of the nonjuror evidence offered by petitioners, that an additional postverdict evidentiary hearing was unnecessary.” Id. at 127, 107 S.Ct. at 2751. The Court reserved the question whether Rule 606(b) might preserve a “common-law exception allowing postverdict inquiry of juror incompetence” after it had been shown by powerful extrinsic evidence. Id. at 125, 107 S.Ct. at 2750.
We have drawn the same line, coupled with the same ambiguous hint that under some circumstances the district court could query the jurors on purely internal matters. See United States v. Wilson, 534 F.2d 375, 378-79 (D.C.Cir.1976) (quoting with approval Government of the Virgin Islands v. Gereau, 523 F.2d 140, 148-50 (3d Cir.1975), which draws such a line, but ultimately affirming on the basis of the trial judge’s discretion in handling claims of irregularity); United States v. Campbell, 684 F.2d 141, 151 (D.C.Cir.1982) (similar). In a case involving mid-trial discovery of pre-deliberation discussions, the Third Circuit seems to have somewhat retreated from Gereau, saying that'it was no basis for holding that “premature jury deliberations, as a form of intrajury influence, can never be the grounds for overturning a verdict.” United States v. Resko, 3 F.3d 684, 694 n. 8 (3d Cir.1993). See also United States v. Bertoli, 40 F.3d 1384, 1395-96 & n. 5 (3d Cir.1994). It is worth noting, in thinking of the Third Circuit’s position, that Rule 606(b)’s ban applies not only to statements made “during the course of the jiffy’s deliberations” but also
to the effect of anything upon that or any other juror’s mind or emotions as influencing the juror to assent to or dissent from the verdict or indictment or concerning the *282juror’s mental processes in connection therewith____
Of course this might encompass only individual jurors’ internal cognitive processes, but Tanner, in upholding the trial court’s refusal to take evidence from jurors as to other jurors’ imbibing and sleeping, clearly states a broader rule, based on its understanding of the common law background norm. Further, other courts besides ours have followed Gereau. See United States v. Tierney, 947 F.2d 854, 869 (8th Cir.1991) (adopting Gereau approach); United States v. Cuthel, 903 F.2d 1381, 1383 (11th Cir.1990) (holding that predeliberation intra-jury communications cannot serve as the basis for a challenge to the verdict).
Preserving the finality of jury verdicts militates strongly in favor of barring post-trial juror assertions of pre-deliberation discussion. The probability of some adverse effect on the verdict is far less than for extraneous influences. “[W]hen there are premature deliberations among jurors with no allegations of external influence on the jury, the proper process for jury decisionmaking has been violated, but there is no reason to doubt that the jury based its ultimate decision only on evidence formally presented at trial.” United States v. Resko, 3 F.3d at 690. And admission of such affidavits would place a powerful weapon in the hands of a juror who senses that his viewpoint is not shared by his fellows — deliberate promotion of pre-deliberation conversations, a move that fellow jurors would be far less likely to report to the court than references to outside materials.
Of course some reformers have proposed completely doing away with the rule against intra-jury discussion of the case before the formal start of deliberations, presumably reasoning that jurors are mature enough to discuss the case during the trial in a tentative way, without settling into final opinions until the case is fully in.1 One panel recommending such changes has argued that allowing the discussions prevents secretive conversations and formation of cliques,2 presumably reasoning that jurors, whose salient common interest must be the trial unfolding before them for several hours a day, are most unlikely to obey the strictures of the standard rule.
But we can resolve this issue without regard to such radical ideas. Even if Rule 606(b) and the common law allow jurors to make post-verdict claims of pre-deliberation discussions, we have, along with other circuits, left trial courts especially broad discretion “ ‘to determine what manner of hearing, if any, is warranted’ ” about intra-jury misconduct. Campbell, 684 F.2d at 151 (quoting Wilson, 534 F.2d at 379). See also, e.g., Resko, 3 F.3d at 690; United States v. Edwards, 696 F.2d 1277, 1282 (11th Cir.1983); Grooms v. Wainwright, 610 F.2d 344, 347 (5th Cir.1980). The decision of the trial court not to hold a post-trial hearing on the subject was clearly within that discretion.
II. Prosecutorial Misconduct
While appellants allege other forms of prosecutorial misconduct not requiring discussion, they focus on the prosecutor’s opening statement. There the lead prosecutor mentioned and attributed to defendants two murders — those of Gerard Bailey and Joel Mays — for which appellants say no evidence was later introduced at trial. Both murders were the subject of counts in the indictment that did not go to the jury: The court dismissed the homicide count for the Bailey killing (which charged only Nugent) on a motion for judgment of acquittal at the end of the trial. And the Mays killing, although charged as racketeering act #35 in the RICO count of the indictment, was also never submitted to the jury. Though appellants acknowledge that failure of proof on a specif*283ic allegation is usually remedied by granting a motion for judgment of acquittal on that allegation (or otherwise preventing or overturning a jury verdict), they argue that this is inadequate here. They want a new trial, first because “it is impossible to remove the taint of these powerful allegations from the eventual jury decision,” and second because the failure of proof was a “deliberate government tactic designed to poison a jury from the very start.” The government disputes appellants’ view that it produced no evidence for the Bailey murder, and argues that the failure to introduce evidence on the Mays murder was not prejudicial.
The trial evidence told the tale of Gerard Bailey’s murder in the context of a feud between the Bailey family and the R Street Crew over drug-marketing territories. The prosecutor said that Gerard Bailey, chieftain of the Bailey clan, had repeatedly warned Crew members to stay out of the neighboring Bailey territory. He said that Bailey, on the day of his death, had threatened Sean Martin (younger brother of Anthony Nugent) and other Crew members with a baseball bat. The prosecutor then said:
And you will hear of the vehemence and the violence of that argument and the threats that Gerard Bailey made. And you will hear that Sean Martin went to Anthony Nugent and told him about what had happened and about what was going on. And you will hear from a friend of Anthony Nugent who was there say that Anthony Nugent told Mr. Sean Martin, “Get Tim [Get him?].” You will hear shortly after this order, Gerard Bailey was found face down in an alley around Second and S Street shot seven times.
The prosecutor’s predictions that the jury would hear all this were never fulfilled; the jury heard no such thing. Although the government claims that it “presented extensive circumstantial evidence concerning this murder,” it presented little from which a reasonable inference could be drawn that Nugent— or any of appellants — was responsible. Detective Angelo Parisi testified (in response to questions by defense counsel) that Gregory Thomas, who worked with Sean Martin as an R Street Crew member, “was seen by a reliable witness shooting and killing Gerard [Bailey],” and that Nugent “wasn’t on the scene” at that point. The investigator said that Sean Martin was also “involved in the direct shooting of Gerard Bailey.” Parisi agreed that it was his theory that “Nugent was responsible for killing Gerard.” But when asked point-blank, “What evidence do you have that Nugent ordered the hit?” Parisi responded, “I myself don’t have any.” To the follow-up question, “Well, who other than you would know, Mr. Parisi?” he responded “I don’t know.” As far as we can tell, there was no evidence at all matching the prosecutor’s prediction that the jury would hear of a friend of Nugent’s saying that Nugent had said to “Get Tim [Get him?].”
The government says its “strongest circumstantial evidence of the connection between Bailey’s death and the B Street Crew” (emphasis added) was that two weeks after Gerard Bailey’s murder Sean Martin was shot and killed in full view of Nugent. Nu-gent then immediately yelled at one of Gerard Bailey’s brothers, “You’re dead.” The next day, Nugent, Williams-Davis, and other R Street Crew members shot up the Baileys’ auto repair shop, killing one person and wounding many others. We agree there is evidence of a link between Gerard Bailey’s murder and the R Street Crew, but we can find none specifically implicating Nugent or any of appellants. The government notes, “As happens on occasion, the government here simply fell short in proving the elements of that offense, for reasons that are not in this record.”
On the Mays killing, the prosecutor was brief — his description takes up only a page out of a 77-page transcript. He said that Mays had tried to sell drugs in the R Street Crew’s territory, that he had been warned by R Street Crew members (not appellants) not to sell there, and that he continued to do so and was murdered by three R Street Crew members — Neil Hilliard, Ronnie Isler, and Andre Williams (Darryl’s and Jeffrey’s brother) — who fled in Darryl Williams’s grey Pathfinder. The prosecutor did not say that any of appellants was responsible for the killing. No further mention of the Mays *284killing was made during the trial. In fact, the three members of the R Street Crew named by the prosecutor — Hilliard, Isler, and Andre Williams — were charged with the murder in D.C. Superior Court, and all entered pleas containing admissions that the government says (without contradiction) “are identical to the description in the government’s opening of the Mays murder.”
Because appellants did not object to the opening statement or seek a mistrial on the ground of taint from an improper opening statement at any point during the trial (including at the close of the government’s case), we review for plain error. F.R.Crim. Pro. 52(b); United States v. Young, 470 U.S. 1, 15, 105 S.Ct. 1038, 1046, 84 L.Ed.2d 1 (1985). To be plain, error must be “clear” or “obvious” and in most eases should result in reversal only if it affected the outcome of the trial. Olano, 507 U.S. at 734, 113 S.Ct. at 1777-78. See also United States v. Saro, 24 F.3d 283, 286-87 (D.C.Cir. 1994).
This court has long recognized that a prosecutor is obliged “to avoid making statements of fact to the jury not supported by proper evidence introduced during trial.” Gaither v. United States, 413 F.2d 1061, 1079 (D.C.Cir.1969). We have formulated a three-part test, of which perhaps the clearest statement is that of United States v. Monaghan, 741 F.2d 1434, 1443 (D.C.Cir.1984), which refers to “the severity of the misconduct, the measures adopted to cure the misconduct, and the certainty of conviction absent the improper remarks.” (Quotations omitted.) See also United States v. Perholtz, 842 F.2d 343, 361 (D.C.Cir.1988) (following Monaghan test); for slightly different phrasing, see Gaither, 413 F.2d at 1079; North, 910 F.2d at 896.
We agree with defendants that mention of two unsubstantiated homicides ordinarily qualifies as severe misconduct, even though, as the government argues, the statements were “isolated” rather than “consistent and repeated misrepresentation^].” Donnelly v. DeChristoforo, 416 U.S. 637, 646, 94 S.Ct. 1868, 1873, 40 L.Ed.2d 431 (1974). The government did not offer any support for its charge that Nugent was responsible for Bailey’s murder, and does not claim to have supported the assertions about the Mays murder in any way. Nor does it offer any reason for the discrepancy, simply urging us not to attribute bad motives to the prosecution. We recognize the difficulties of coordinating proof in a long case involving many counts. See Frazier v. Cupp, 394 U.S. 731, 736, 89 S.Ct. 1420, 1423, 22 L.Ed.2d 684 (1969) (“Many things might happen during the course of the trial which would prevent the presentation of all the evidence described in advance. Certainly not every variance between the advance description and the actual presentation constitutes reversible error, when a proper limiting instruction has been given.”). But obviously the government should be especially careful, where extraordinarily serious charges are at stake, to avoid gaps between prediction and evidence.
As for curative instructions, the district court told the jury in preliminary instructions (before the opening statements) that opening statements were not evidence. The court repeated that instruction in the middle of the prosecutor’s opening statement. Finally, in its charge to the jury, it instructed that statements and arguments of counsel are not evidence. Defendants did not request a more specific limiting instruction. In North, we held that the general instruction that statements of counsel were not evidence was enough to cure inappropriate references in a prosecutor’s closing argument, 910 F.2d at 897, although we noted that such an instruction would not suffice in “particularly egregious” cases, where specific curative instructions might be needed, id. at 897-98 n. 33. We do not believe this to be a particularly egregious case, because of the full context of the misconduct, to which we now turn.
The third criterion looks in part to specific features in the context of the misconduct, and also to the strength of the government’s case, for a practical assessment of whether the misconduct was likely to have had any impact. See, e.g., Monaghan, 741 F.2d at 1443; Perholtz, 842 F.2d at 361; Gaither, 413 F.2d at 1079. In some respects the error here gave defense counsel a club with which to beat the government. Nugent’s counsel, *285by questioning Detective Parisi so as to bring out the lack of proof against Nugent, was able to use the variance between the government’s opening and its proof to sow doubt of the prosecution among the jurors — both during his questioning and at several points during his forceful summation. See United States v. Monks, 774 F.2d 945, 955 (9th Cir. 1985); United States v. Somers, 496 F.2d 723, 739 n. 30 (3d Cir.1974). Further, the length of time between the prosecutor’s opening statement and jury deliberations— five months — makes it unlikely that specific allegations in the opening profoundly influenced those deliberations. Finally, the evidence of defendants’ use of deadly violence was overwhelming. See pages 274-75 above.
In sum, we do not find there was the sort of likelihood, required for plain error, that the excesses of the prosecutor’s opening statement substantially affected the outcome of the trial, much less that it “seriously affeet[ed] the fairness, integrity or public reputation of judicial proceedings.” Olano, 507 U.S. at 732, 113 S.Ct. at 1776 (quotations omitted).
III. Continuing Criminal Enterprise Instruction
A. Argument for Specific Instruction About Suppliers
Williams-Davis, Nugent, and Darryl Williams argue that the district court should have instructed the jury that it could not consider various drug suppliers — Alvin Buck-halter, Sonny Knox, Jaime (Jimmy) and Billy Bynoe, a man named “Young Lew,” and Claude Juggins — among those that they supervised or managed for purposes of triggering liability under the Continuing Criminal Enterprise statute, 21 U.S.C. § 848. Their basic theory is that suppliers cannot, in the nature of things, occupy the sort of subordinate or “managee” position necessary under the statute. Section 848 defines continuing criminal enterprise as follows:
For purposes of subsection (a) of this section, a person is engaged in a continuing criminal enterprise if—
(1) he violates any provision of this sub-chapter or subchapter II of this chapter the punishment for which is a felony, and
(2) such violation is a part of a continuing series of violations of this subchapter or subchapter II of this chapter—
(A) which are undertaken by such person in concert with five or more other persons with respect to whom such person occupies a position of organizer, a supervisory position, or any other position of management, and
(B) from which such person obtains substantial income or resources.
21 U.S.C. § 848(e) (emphasis added). Because appellants did not object to the instruction on this issue (indeed, their proposed instruction differed only slightly from what the trial court gave), review is for plain error only.
On its face the language of § 848(c) does not seem to suggest that suppliers are per se excluded from the circle of possible managees. If a supplier appears generally to take specific direction from his customer, in a manner indistinguishable from that of other subordinates, we do not see why the role of supplier should make a difference. Certainly we do not think Congress intended the courts to limit the managerial relationship to persons in the same “firm” as the defendant. Vertical relationships in the world of criminal enterprises do not seem as readily divisible among the various possibilities — single firm (with an employer-employee relation), long-term agency relations, longterm contracting and spot contracting — as are those of the lawful economy. If the defendant specifies a person’s activities in adequate detail, cf. United States v. Delgado, 4 F.3d 780, 785 (9th Cir.1993), that should be enough.
Appellants’ theory excluding suppliers turns on what strikes us as too broad a reading of two cases from the Ninth Circuit, United States v. Jerome, 942 F.2d 1328 (9th Cir.1991), and Delgado. In Jerome, 942 F.2d at 1331, the court sensibly read the statutory language “or any other position of management” to mean that an organizer must exercise some sort of managerial responsibility. The later decision in Delgado explained the outcome as a matter of syntax. Applying a *286sort of reverse ejusdem generis (where the general term reflects back on the more specific rather than the other way around), it said that the phrase “A, B, or any other C” indicates that A is a subset of C, so that the reference in § 848(c) to an “organizer” or a holder of a “supervisory position” requires some sort of managerial capacity. Delgado, 4 F.3d at 786. Jerome went on to say that a defendant does not qualify as a manager simply by setting up “a system of supply,” and that “[t]o be an organizer within the sense of the statute more is required than simply being a steady customer.” 942 F.2d at 1331. On the evidence presented in that case, two suppliers proffered by the government as managees could not count as such. Similarly, in Delgado, the court held that a dealer’s customers could not count toward the five without further evidence of a defendant’s management, but emphasized that an “organizer” did not have to “control” others — -just manage them. 4 F.3d at 785.
Thus Jerome and Delgado simply require an actual managerial relationship, a requirement that the Ninth Circuit said was not displaced for suppliers or customers. Just so. Cases in this circuit and another agree. United States v. Mitchell, 49 F.3d 769, 772 (D.C.Cir.1995); United States v. Ward, 37 F.3d 243, 248 (6th Cir.1994). But the analysis does nothing to preclude suppliers from counting if their conduct is managed closely enough. Cf. United States v. Phibbs, 999 F.2d 1053, 1086 (6th Cir.1993) (finding no error in trial court’s refusal to charge that mere buyer-seller relation was not enough to establish management relation, as none of the people the government said defendant had managed were mere buyers or sellers). Indeed, the evidence shows that Juggins may well have been managed by at least Williams-Davis and Nugent. Juggins testified that he would get money from Williams-Davis and Nugent to give to Jimmy Bynoe for cocaine, and would typically hold the cocaine at his apartment for either of the two to pick up. On occasion, however, he would take the drugs to them or to someone else at their direction. He was paid as Williams-Davis directed.
Appellants also argue that the district court should have given the jurors a specific instruction requiring them to agree unanimously on the identity of each of the five people whom any defendant managed. Our circuit has rejected any such requirement. United States v. Harris, 959 F.2d 246, 254 — 55 (D.C.Cir.1992). In Jerome the court applied a different rule in different circumstances, requiring such an instruction where the prosecutor had submitted a specific list of names to the jury, some of whom could not properly have been found to be managees. 942 F.2d at 1331. As that circumstance is not present here, we needn’t consider whether we would distinguish Harris on that ground.
Appellants object that the potential for juror confusion was increased by references in the prosecutor’s closing statement that, appellants say, invited the jurors to find suppliers to be managees, and by the length and complexity of the trial. In fact the references that appellants regard as inviting such a finding seem much more naturally understood as referring to defendants’ local flunkies, not to their remote suppliers:
It is the entire group I told you about at the start. From the runners to the lieutenants to the people who ran the stash houses to the people who brought the drugs in to the people who banked the money to the people who bought the cars to the people who brought the weapons in to the people who did the murders. Ladies and gentlemen, this is what shows they were a large drug conspiracy; that they were a continuing criminal enterprise operating here in the streets of Washington, D.C.
(Emphasis added.) As to the length and complexity of the trial, it is hardly the government’s fault that the appellants chose to run a large, complex drug operation for at least seven years. In its brief, the government points to 43 people identified at trial as either lieutenants, runners, packagers, or transporters, all of whom could be considered managees. Under the circumstances, the likelihood that any of the jurors relied on a non-managed supplier to reach the number five is remote indeed.
*287B. Ex Post Facto Claim
Appellants argue that the trial court’s refusal to give a requested charge on the timing of their violation of the CCE statute’s “Super CCE” section violated their rights under the ex post facto clause. Because there was no possibility that the jury finding could have rested solely on conduct preceding the critical date, we reject the claim.
Congress added the Super CCE clause to the CCE statute in 1986. Anti-Drug Abuse Act of 1986, Pub.L. No. 99-570, § 1258, 100 Stat. 3207. While § 848(a), the normal CCE clause, permits life imprisonment upon conviction of its violation, the new § 848(b) mandates it if additional requirements are met. That clause, which took effect October 27, 1986, states:
(b) Life Imprisonment for engaging in continuing criminal enterprise Any person who engages in a continuing criminal enterprise shall be imprisoned for life and fined in accordance with subsection
(a) of this section, if—
(1) such person is the principal administrator, organizer, or leader of the enterprise or is one of several such principal administrators, organizers, or leaders; and
(2) [various quantitative thresholds, relating to the volume of drugs and gross receipts of the enterprise, are met].
21 U.S.C. § 848(b). In a trial brief on the CCE statute, Darryl Williams argued that, to avoid offending the ex post facto clause, U.S. Const, art. I, § 9, cl. 3, “the prosecution must prove that the defendant satisfied all super CCE elements after October 27,1986.” In his Requested (Jury) Instruction No. 2 (concerning continuing criminal enterprise), Williams included the sentence, “All of these requirements must have been satisfied by actions taking place after October 27, 1986, the day the law went into effect.” Counsel for Williams made the point again orally to the district court. We assume arguendo that the similarly situated defendants can free ride on Williams’s motion, which they would be able to do if the trial court told counsel that an objection by one defendant would be considered on behalf of all unless disclaimed. See Charles A. Wright, Federal Practice and Procedure § 499, at 805 (1982).
In its instructions on CCE (which included Super CCE), the district court did not mention a required time frame (or any time frame at all) for a CCE violation. But it did instruct that in order to find a CCE violation (charged in count 4 of the indictment), the jury had to first find a conspiracy among the defendants to distribute drugs in violation of 21 U.S.C. § 846 (charged in count 3).3 In turn, in the instructions on the conspiracy count, the court told the jury that to convict they must find that the conspiracy existed “beginning in or about May of 1983 and continuing thereafter until and including March 26, 1991,” a period nearly five full years beyond the start of liability under Super CCE. In addition, the court gave the jurors a form on which they could indicate which two other predicate acts, apart from the conspiracy, formed the basis for a CCE conviction. (The district court stated that three predicate acts were required.) The jury convicted on the CCE count and found, as the predicate acts for each defendant other than the conspiracy, crimes committed exclusively after October 27,1986.4
A law violates the ex post facto clause if it is (1) retrospective (that is, applies to events occurring before its enactment) and (2) disadvantages the offender affected by it, as by imposing a harsher penalty than a law in effect on the date of the offense. Weaver v. Graham, 450 U.S. 24, 30-31, 101 S.Ct. 960, 965-66, 67 L.Ed.2d 17 (1981); see also Miller *288v. Florida, 482 U.S. 423, 430, 107 S.Ct. 2446, 2451, 96 L.Ed.2d 351 (1987) (reaffirming Weaver test). As Super CCE seriously increased the risk of a life sentence (from a possibility to a certainty), it is harsher than the prior law. Cf. United States v. Bader, 956 F.2d 708, 709 (7th Cir.1992) (reasoning that adverse changes in federal Sentencing Guidelines after a crime is committed do not violate the ex post facto clause so long as they do not extend the sentencing exposure established by statutory offense categories). The change in the statute, therefore, can only be applied to a continuing offense if the illegal conduct continued into the period after enactment. See United States v. Torres, 901 F.2d 205, 226 (2d Cir.1990); United States v. Johnson, 537 F.2d 1170, 1175 (4th Cir.1976); United States v. Campanale, 518 F.2d 352, 365 (9th Cir.1975). The question here is whether an explicit instruction on timing was needed. Following most of our sister circuits, we review the issue de novo. See, e.g., United States v. Walker, 27 F.3d 417, 419 (9th Cir.1994); United States v. Cabrera-Sosa, 81 F.3d 998, 1001 (10th Cir.1996); Ha-mama v. INS, 78 F.3d 233, 235 (6th Cir. 1996). But see Orellana v. Kyle, 65 F.3d 29, 33 (5th Cir.1995) (saying district court did not “abuse its discretion” in rejecting ex post facto claim).
Appellants argue that because the trial court instructed that to convict the jury should find the conspiracy began about May 1983, it is “possible that the CCE conviction rested at least in part on conduct that occurred prior to the statute’s effective date” and therefore violates the ex post facto clause. For this to have happened, the jury would have had to have found that the defendants (1) were part of a conspiracy to distribute drugs from about May 1983 to March 26, 1991, (2) led the conspiracy for some time before October 27, 1986, (3) committed the specific predicate acts that were found (all after that date), but somehow — by choice or ouster or some other mishap — dropped from their leadership roles after that date. Appellants point to no shred of evidence of any such abdication by them or rebellion by their underlings. As a practical matter, the risk of such a bizarrely configured jury finding was zero. Thus, although we reviewed under a plain error standard in Mitchell, 49 F.3d at 772, its conclusion controls. There the evidence of leadership after the date of enactment, coupled with a special verdict form finding 14 predicate acts by defendant Campbell after October 27, 1986, left the court in “no doubt” that Campbell was not prejudiced by the absence of a specific instruction requiring a leadership role after the date of enactment. Id. at 781. Here too the omission was harmless.
We note that the Second Circuit declined to find harmless error in Torres, even though the evidence at trial made it highly improbable that the jury found defendants had given up their leadership role after October 27, 1986. 901 F.2d at 228-29. But there the trial court had submitted a special verdict form that affirmatively directed the jury’s attention to the period before the enactment of Super CCE: “ Was [the particular defendant] a principal administrator, organizer or leader of the continuing criminal enterprise at some time during the one-year period from June 2k, 1986 to June 28, 1987V ” Id. at 226 (quoting jury verdict form and adding emphasis); see id. at 229 (holding that despite strong evidence, court would reverse where instruction on its face violated ex post facto clause). Thus, assuming arguendo that Torres might provide a basis for distinguishing our own decision in Mitchell, the distinguishing feature is absent here.
IV. Individual Arguments
A. Nugent’s § 924(c)(1) Convictions
Nugent was convicted under 18 U.S.C. § 924(e)(1) of two counts of using or carrying a firearm during the commission of a crime of violence or drug trafficking. For both counts, the underlying offense was the § 846 drug conspiracy of count 3. The government agrees with Nugent that one of these convictions must be vacated under our recent holding in United States v. Anderson, 59 F.3d 1323, 1334 (D.C.Cir.1995) (en banc), that a single predicate crime can support only one § 924(c)(1) violation. For purposes of recidivism statutes it may make a difference which count we vacate. If the jury delivered sequential verdicts, we think it would make *289sense to pick the later one, as only it would violate Anderson. But as that appears not to be the case, we vacate the conviction on count 107, which involves the later of the acts charged as violating § 924(c)(1).
B. Restrepo’s Jencks Act and Brady Arguments
1. Jencks Act
Evidence at trial showed that one Jimmy Bynoe (brother of the Billy Bynoe referred to earlier as a supplier) was defendant Restrepo’s boyfriend and business associate, acting under her direction in their dealings with the go-between Claude Juggins to supply the R Street Crew. Over two and a half years, they sold the Crew between nine and ten million dollars’ worth of cocaine. Bynoe was arrested on June 22, 1990 at Union Station with three kilograms of cocaine for delivery to Juggins. According to evidence and government representations at trial and in its brief, Bynoe agreed to cooperate with the government, but then skipped bond and fled to Panama, with which we evidently have no extradition treaty. So Bynoe never testified. Through Juggins, the government introduced at trial a number of recorded telephone calls involving Bynoe and Restrepo, as well as other second-hand statements of Bynoe. See F.R.E. 801(d)(2)(E). All of these statements predated Bynoe’s arrest. Alba Restrepo claims that admission of his eoconspirator statements triggered the government’s duty under the Jencks Act, 18 U.S.C. § 3500, to provide any statements made by him to the government after his arrest (and apparently his plea agreement as well). It is clear that Restrepo sought these items, and, if counsel failed to mention the Jencks Act (which is unclear), the government makes no point of the omission. Whether the Jencks Act applies under these circumstances is a question of statutory construction that we review de novo. See United States v. Anderson, 39 F.3d 331, 348 (D.C.Cir.1994) (reviewing de novo whether Jencks Act requires government to produce a trial transcript that it has not requested or received from the court reporter).
Federal Rule of Criminal Procedure 16(a)(2) prohibits discovery of statements by government witnesses or prospective government witnesses except as provided in the Jencks Act. That statute provides:
§ 3500. Demands for production of statements and reports of witnesses
(a) In any criminal prosecution brought by the United States, no statement or report in the possession of the United States which was made by a Government witness or prospective Government witness (other than the defendant) shall be the subject of subpoena, discovery, or inspection until said witness has testified on direct examination in the trial of the ease.
(b) After a witness called by the United States has testified on direct examination, the court shall, on motion of the defendant, order the United States to produce any statement ... in the possession of the United States which relates to the subject matter as to which the witness has testified.
18 U.S.C. § 3500.
Because Bynoe was never “called” by the government, Restrepo uses elements of the Federal Rules of Evidence to argue that admission of his statements was the equivalent of his being called. That admission occurred under Rule 801(d)(2)(E), which defines statements by eoeonspirators during and in furtherance of the conspiracy as not being hearsay. In addition, Rule 806 says that when a statement is admitted under Rule 801(d)(2)(C), (D), or (E), the opposing party may impeach the statement with “any evidence which would be admissible for those purposes if the declarant had testified as a witness.” If the equation of a declarant’s 801(d)(2)(E) statement with conventional testimony is good enough for Rule 806, Restrepo argues, it should be good enough to trigger the Jencks Act. As far as we can tell, we are the first court of appeals to address this argument.
We dealt with a similar issue in United States v. Tarantino, 846 F.2d 1384, 1418 (D.C.Cir.1988). The defendant there sought statements by a coconspirator who was listed among the government’s prospective witnesses but did not testify at trial. The defendant pointed out that a statement admit*290ted under Rule 801(d)(2)(E) becomes, for hearsay purposes, a statement of the defendant, and that a defendant is entitled to obtain his own statements under F.R.Crim. Pro. 16(a)(1)(A). Reading the two rules together, the appellant argued that “because the coeonspirator’s statements may be treated as the defendant’s own for purposes of hearsay analysis, ... they should be discoverable in the same manner as the defendant’s own statements.” 846 F.2d at 1418. We rejected the theory, on the ground that Rule 16(a)(1)(A) could not be read to permit such discovery, implicitly because it would violate the balance chosen by Congress between the defendant’s interest in use of non-witness materials and the government’s interest in their non-disclosure. Id. Several other circuits have reached the same result. See, e.g., United States v. Roberts, 811 F.2d 257, 258-59 (4th Cir.1987) (en banc); United States v. Orr, 825 F.2d 1537, 1541 (11th Cir.1987) (not interpreting the Jencks Act).
Of course in Tarantino the coconspirator’s statements were not introduced into evidence at trial, so the exact issue was different. But the principle-of Tarantino surely was broader: merely because one set of rules (internally consistent, one hopes) makes two distinct items equivalent for some specific purpose, it does not follow that they are equivalent for all related purposes. That a declarant’s statement becomes a statement of the defendant under F.R.E. 801(d)(2)(E) does not mean it becomes the defendant’s statement for purposes of F.R.Crim. Pro. 16(a)(1)(A), Tarantino; that a declarant is treated as a witness for purposes of Rule 801(d)(2)(E) or Rule 806 does not mean he becomes one for purposes of the Jencks Act.
The automatic subjection to the Jencks Act of statements by declarants embraced by Rule 801(d)(2)(C), (D), and (E) would carry broad implications. As we have said, that Act represents Congress’s balance of the defendant’s need for such statements for impeachment purposes against the government’s interests — “concern for witness intimidation, subornation of perjury, and other threats to the integrity of the trial process.” Tarantino, 846 F.2d at 1414. The fear is that if witness statements were disclosed before their testimony, witnesses could be threatened or bribed to change their stories and denounce their previous statements. Of course the timing aspect of that balance would be explicitly upset under Restrepo’s approach in any case where the government planned to call a coconspirator but introduced a statement of his in furtherance of the conspiracy earlier in the trial. Even for the coconspirator that is not expected to be called, the Fourth Circuit has reasoned that the risk of intimidation argues powerfully against disclosure of statements made to the government by a non-testifying coconspirator. Roberts, 811 F.2d at 259 (adopting the analysis of Wilkinson, J., dissenting in United States v. Jackson, 757 F.2d 1486,1492-94 (4th Cir.1985)).
Finally, we note that our hewing to the standard meaning of § 3500 by no means leaves the defendant bereft of means for discovering a declarant’s statements to the government. If a declarant contradicted himself on a key point, then Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 1196, 10 L.Ed.2d 215 (1963), would likely require disclosure. Accordingly, we reject Restrepo’s Jencks Act claim and turn to the one she makes under Brady.
2. Brady Arguments
Restrepo argues that the government was obliged under Brady to disclose the material also sought under the Jencks Act. (She apparently does not make a separate argument based on F.R.Crim. Pro. 16(a)(1)(C), which requires disclosure of documents “material to the preparation of the defendant’s defense.”) The prosecution certainly has an affirmative duty to disclose material evidence “favorable to an accused,” Brady, 373 U.S. at 87, 83 S.Ct. at 1196, including evidence that could be used to impeach a witness, Giglio v. United States, 405 U.S. 150, 154-55, 92 S.Ct. 763, 766, 31 L.Ed.2d 104 (1972). The Supreme Court has defined material evidence favorable to the defendant to mean ‘“there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.’ ” Kyles v. Whitley, — U.S. -, -, 115 S.Ct. *2911555, 1565, 131 L.Ed.2d 490 (1995) (quoting United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 3383-84, 87 L.Ed.2d 481 (1985) (opinion of Blackmun, J.)); see also United States v. Smith, 85 F.3d 646, 646 (D.C.Cir.1996) (denying petition for rehearing). The Third Circuit has followed the Ninth in holding that “[w]e think it is unwise to infer the existence of Brady material based upon speculation alone---- ‘[U]nless defendant is able to raise at least a colorable claim that the [disputed material] contained evidence favorable to [him] and material to his claim of innocence or to the applicable punishment,’ ” no Brady violation will be established. United States v. Ramos, 27 F.3d 65, 71 (3d Cir.1994) (quoting United States v. Griffin, 659 F.2d 932, 939 (9th Cir.1981)). We also adopt that approach.
Except for bare speculation, Restrepo has nothing to suggest the existence of favorable materials. Many of Bynoe’s statements introduced at trial were recorded as he and others went about committing the crimes, and it seems improbable that these would be vulnerable to impeachment. All the statements of his that were admitted were made before his arrest, so that they could not have been affected by his later plea agreement. The prosecutor, who had the responsibility under the Brady framework to make the first determination about whether material was exculpatory, United States v. Brooks, 966 F.2d 1500, 1504 (D.C.Cir.1992) (citing Pennsylvania v. Ritchie, 480 U.S. 39, 59, 107 S.Ct. 989, 1002, 94 L.Ed.2d 40 (1987)), said in court that the defense “would not be happy” with Bynoe’s statements to the government. Restrepo gives us no reason to doubt it.
Accordingly, appellants’ convictions are all affirmed, with the exception of Anthony Nu-gent’s second conviction under 18 U.S.C. § 924(c)(1), which is vacated along with the sentence attributable thereto.
So ordered.