This appeal concerns primarily the validity of a verdict returned in a criminal trial *823by an eleven-person jury, after a juror was excused during deliberations pursuant to the recently amended Rule 23(b) of the Federal Rules of Criminal Procedure. Richard Stratton, Steven Parness, Leonard Parness, and Bernard Farbar appeal from judgments of conviction entered in the District Court for the Southern District of New York (Constance Baker Motley, Chief Judge) following a jury trial. All appellants but Stratton were convicted of conspiracy either to distribute drugs or possess drugs with intent to distribute them, in violation of 21 U.S.C. § 846 (1982).1 All appellants were convicted of conspiring to import hashish, in violation of 21 U.S.C. § 963 (1982), and of importing hashish, in violation of 21 U.S.C. §§ 952, 960 (1982). Stratton was also convicted of engaging in a continuing criminal enterprise, in violation of 21 U.S.C. § 848 (1982), and cited for criminal contempt for his conduct during the course of the trial.2 In addition to the eleven-person jury issue, all appellants but Farbar challenge the sufficiency of the evidence to support their convictions and certain evidentiary rulings. Stratton challenges certain of the jury instructions and the summary nature of the criminal contempt proceeding.3 Because each of these contentions is without merit, we affirm.
I. Background
The Government’s proof at trial demonstrated that appellants, under the leadership of Stratton, were responsible for importing a major hashish shipment into the United States from Lebanon in 1981. Stratton became acquainted with the international drug business in the mid-1970’s. Shortly thereafter, Farbar became his assistant. In the late 1970’s, Stratton met Mohamad Berro, a former Lebanese customs inspector, who, with his son Nassif, was a substantial supplier of Lebanese hashish. In January 1980, Stratton and Farbar planned to import hashish from Lebanon, with the Berros as their source of supply. The shipment, purportedly of machine tools, went by air from Lebanon to Tokyo, Japan, and then to Kennedy Airport in New York. Because of the shipment’s unusual itinerary, Customs officials inspected it and discovered 2,000 pounds of hashish. At that time, the Government could not identify the responsible parties.
Stratton resolved to find a better cover for his next importation of Lebanese hashish. For this purpose, he brought Steven Parness and his father, Leonard, the owner of a New Jersey based trucking concern, into the conspiracy. The Parness Trucking Company had a business relationship with a company that imported dates from the Middle East, the Bordo Products Company of Chicago. It was decided that an importation of 150,000 pounds of dates by Bordo would be used to camouflage importation of more than seven tons of hashish and hashish oil.4
*824In preparation for the second shipment, Mohamad and Nassif Berro visited New York in April of 1980. They attended a dinner meeting with Stratton, his wife, Gabrielle, and Farbar. Sobhi Hammoud, a distant relative of the elder Berro, acted as his interpreter. Mohamad Berro told Ham-moud that Stratton and Farbar had been good customers of his in the date business for some time. Hammoud acted as interpreter for Mohamad Berro at a second dinner meeting with Stratton and Farbar at which the date business was again discussed. Berro invited Stratton to come to Lebanon to inspect the goods. Stratton’s passport shows that he visited Lebanon in July of 1980.
Mohamad Berro returned to New York in September 1980. He and Hammoud met with the Strattons, Farbar, and Steven Parness. Parness displayed a bag of dates and told Berro that the sample demonstrated the quality of dates desired by his customer, the Bordo Company. Berro agreed to provide dates of that quality. Berro later shipped a sample of dates to New York. The Bordo Company found them to be of acceptable quality. In January 1981, Bordo formally confirmed an agreement to purchase 150,000 pounds of Iraqi dates from the Berros.
In January 1981, the Strattons went to Lebanon at Mohamad Berro’s request. Stratton sent for Farbar, who smuggled $50,000 in cash into Lebanon as the first downpayment on the illicit hashish shipment. In February 1981, the dates and the hashish were loaded on two ships in Beirut, Lebanon. The total shipment consisted of six containers. Within each container, cartons of hashish were surrounded by layers of cartons of dates.
In April 1981, the two ships arrived in New York. Leonard Parness had been assigned by Stratton to pick up the shipment but was hesitant out of fear of discovery by Customs officials. Stratton paid Leonard Parness $600,000 to convince him to pick up the shipment. Customs officials accompanied the shipment to the warehouse of the Parness Trucking Company. They made a cursory inspection, and, finding only dates, they left. After initial delivery, the Parnesses moved the hashish to a “stash-house” located on Staten Island.
In May 1981, Mohamad Berro traveled to New York to receive payments for successful delivery of the hashish. On separate occasions, Stratton gave him $20,000, $180,-000, and $30,000. As Stratton was making the last of these payments, Steven Parness complained that Berro was receiving more than his share. Stratton told Parness to keep silent, paid Berro the $30,000, and indicated that profits from the sale of the hashish oil would be divided solely between Stratton and Berro.
Stratton made plans to transport the hashish to Canada for sale. He agreed that as profits became available he would give Berro’s share to Hammoud, who would transport it from Canada to Lebanon. In August of 1981, Hammoud went to Canada at Stratton’s direction. He was instructed to phone Michelle Siegel, Gabrielle Stratton’s daughter, to locate Gabrielle and to pick up the money from Gabrielle.5 Following this procedure, Hammoud received $270,000 and transported it to Lebanon. Shortly thereafter, Gabrielle Strat-ton gave $300,000 to Nassif Berro, who took the money to his father.
In September 1981, Hammoud made a second trip to Canada. He contacted Sie-gel and was eventually given $270,000 by Gabrielle Stratton and Terry Heddon, a Canadian pilot who worked for Richard Strat-ton. During October, Hammoud made his third trip to Canada and received $212,000 from Gabrielle Stratton and Michelle Sie-gel. Gabrielle informed Hammoud that this was to be the last of the payments to Berro.
Mohamad Berro, unwilling to see the payments end, went with Hammoud to Nassif Berro’s home in Miami in November *825of 1981. The group eventually located the Strattons in the Bahamas. On two occasions, Gabrielle Stratton hung up on Ham-moud. Richard Stratton then called Ham-moud and threatened to kill Hammoud’s family if Hammoud continued to bother him.
Mohamad Berro and Hammoud then returned to New York, where they met with the Parnesses. All parties complained that Stratton was refusing to pay out any more money. The Parnesses also noted that they were still awaiting Stratton’s instructions regarding disposition of the last ton of hashish in storage. Upon his own return to New York, Stratton made a final $10,000 payment to placate Berro.
In June 1982, Hammoud and Nassif Ber-ro were arrested in California on unrelated drug charges. Hammoud agreed to cooperate with the Government and ultimately provided the core of the Government’s proof at trial.
In September 1982, Hammoud induced Farbar to meet with an undercover agent of the Drug Enforcement Administration (DEA), Martin Maguire. Agent Maguire posed as a drug dealer wishing to locate the last ton of hashish held in storage by the Parnesses. Maguire suggested that the proceeds from the sale could be used to bail out Nassif Berro and ensure that he would not cooperate with the Government. Farbar agreed to talk with the Parnesses about the last of the hashish. Although the Government attempted to record this conversation, a mechanical failure prevented its introduction as evidence at trial.
The Government was successful, however, in recording three further conversations involving Farbar. During a car ride, Farbar told Hammoud that he had done his best to locate the Parnesses but had been unsuccessful. He discussed the hashish deal with Hammoud, including his own trips to Lebanon, and wondered what effect the Lebanese war would have on the hashish business.
At a dinner meeting with Hammoud and Maguire, Farbar again explained that he had been unable to reach the Parnesses. He said that Stratton might have paid some money to Ayala Shibley, a relative of the Berros living in Texas. He said he hoped Nassif Berro would not cooperate with the Government. Farbar then discussed the course of the hashish transaction. He recalled Leonard Parness’s original reluctance to pick up the hashish shipment. He confirmed that Stratton had paid Berro $1.3 million but had probably reneged on a promise to pay additional money. He speculated that the last ton of hashish probably remained at the stash-house on Staten Island.
At a final meeting with Hammoud, Far-bar told him that he had learned from Gabrielle Stratton that Nassif Berro would probably cooperate with the Government. Farbar said he still hoped this would not occur and again expressed concern about the effect of the Lebanese war on the hashish business.
In May 1983, DEA agents obtained a warrant to search the stash-house on Staten Island. The search uncovered a large wooden pallet of the same type as the one used to unload the hashish in April of 1981. Although no hashish was present, the DEA agents found traces of tetrahydrocannabi-nol, the active agent in hashish.
II. The Jury Charge
In order to convict Stratton of engaging in a continuing criminal enterprise, the jury had to find that Stratton committed “a continuing series of [narcotics] violations,” 21 U.S.C. § 848(b)(2), which we have held means three or more violations, see United States v. Young, 745 F.2d 733, 747 (2d Cir.1984), cert. denied, — U.S.-, 105 S.Ct. 1842, 85 L.Ed.2d 142 (1985). The Government urged that Stratton had committed the following narcotics violations: conspiracy to import hashish, as charged in the indictment; importation of hashish, as charged in the indictment; importation of the hashish discovered at Kennedy Airport in January of 1980; telephone use violations under 21 U.S.C. § 843(b) (1982); and distribution of, and possession with intent *826to distribute, hashish in violation of 21 U.S.C. § 841(a)(1) (1982). Stratton challenges three aspects of the trial court’s instructions on the section 841 offense.
First, Stratton urges that the jury should have been instructed that it could not find him guilty of the predicate offense of distributing hashish absent proof of particular acts of distribution. However, such proof is not required to establish a section' 841 violation. The evidence need show only that the defendant caused a distribution to occur. The Government’s proof showed that Stratton transported hashish to Canada for intended distribution and soon thereafter received substantial amounts of money. After going to Canada, Stratton made payments to Berro in excess of $1 million and bought property in Texas worth more than $200,000. The jury was entitled to infer that Stratton accomplished his purpose and converted drugs into money. See Bentley v. Cox, 508 F.Supp. 870, 875 (E.D.Va.1981) (jury may infer from possession of currency that drugs were sold). This Court has held that an indictment alleging illegal sale of narcotics need not specify the identity of the recipient or the precise place and circumstances of the offense because these items are not essential elements of the offense. See Sirico v. United States, 350 F.2d 310 (2d Cir.1965); United States v. Spada, 331 F.2d 995 (2d Cir.), cert. denied, 379 U.S. 865, 85 S.Ct. 130, 13 L.Ed.2d 67 (1964).
Second, Stratton argues that the trial court improperly failed to instruct the jury on the elements of a section 841 violation. Although he failed to object to this portion of the charge, he argues that failure to instruct on the elements of a crime is plain error warranting reversal. However, the trial court instructed that the jury could not find Stratton guilty of the section 841 predicate offense unless it found that he distributed hashish or possessed hashish with intent to distribute. The Court gave proper guidance on the meaning of “intent.” The Court did not give instructions on the meaning of “distribution” or “possession.” Since these terms are clear enough, detailed instructions were not required absent a pertinent request. If Stratton wished to raise a technical legal issue (e.g., whether particular acts are sufficient to constitute constructive possession), he was required to alert the trial judge to his concern.
Third, Stratton notes that he could not be guilty of two predicate offenses based upon section 841(a)(1) unless the Government proved a possession distinct from that involved in a distribution. See United States v. Young, supra, 745 F.2d at 754. He argues that the trial court’s failure to so instruct was plain error. We disagree. The instruction did not omit an element of the section 848 offense. At worst it failed to explain an aspect of using section 841 violations as predicate offenses, a matter not critical in this case since the jury was entitled to find three predicate violations without cumulating possession of drugs and distribution of the same drugs. Cf. United States v. Mowad, 641 F.2d 1067 (2d Cir.), cert. denied, 454 U.S. 817, 102 S.Ct. 94, 70 L.Ed.2d 86 (1981); United States v. Dixon, 536 F.2d 1388 (2d Cir.1976).
III. Sufficiency of the Evidence
A. Stratton
Stratton challenges in two respects the sufficiency of the evidence to support his continuing criminal enterprise conviction. First, he argues that the distribution and possession with intent to distribute offenses should never have been submitted to the jury as predicate acts because any distribution that might have occurred took place in Canada and not in the United States. With regard to possession with intent to distribute, the location of the distribution is irrelevant as long as the act of possession occurs within the United States. See United States v. Muench, 694 F.2d 28, 33 (2d Cir.1982), cert. denied, 461 U.S. 908, 103 S.Ct. 1881, 76 L.Ed.2d 811 (1983). With regard to distribution, we have no occasion to decide whether a defendant who sells narcotics in a foreign country can *827ever be guilty of a section 841 violation or what prior acts connected with a distribution are sufficient to establish a violation. This point has not been properly preserved for appellate review. The defendant’s only objection to submitting the section 841 offenses to the jury as predicate offenses was the particularity objection, which has been rejected. Stratton never sought to withdraw the section 841 violations from the jury for lack of sufficient evidence of distributions in the United States. Therefore, since the Government adduced sufficient evidence of at least three other predicate offenses,6 the continuing criminal enterprise conviction must stand regardless of whether the evidence of a section 841 distribution is sufficient. See United States v. Mowad, supra, 641 F.2d at 1073-74; United States v. Dixon, supra, 536 F.2d at 1401-02.
Stratton also argues that the evidence is insufficient to support a finding that he organized, supervised, or otherwise managed five people in his scheme to violate the drug laws, as required by section 848(b)(2)(A). The Government argues that Stratton supervised eight people: Bernard Farbar, Terry Heddon, Gabrielle Stratton, Michelle Siegel, Leonard Parness, Steven Parness, the “stash-house” guard, and So-bhi Hammoud. Stratton does not challenge the sufficiency of the evidence of supervision of Farbar and Heddon. Therefore, since no specific objection was made to submitting particular names to the jury, Stratton’s section 848 conviction must stand if the evidence is sufficient to support the inference that he supervised at least three other people. See United States v. Mowad, supra; United States v. Dixon, supra.
With regard to Gabrielle Stratton, the Government’s proof showed that she attended meetings at which the conspirators discussed their plans and acted as a courier for her husband. While in Canada, Gabrielle Stratton helped transmit Mohamad Berro’s share of the drug profits by making payments in excess of $1 million to Hammoud and Nassif Berro. Stratton does not deny his wife’s participation but argues that she was an equal partner, rather than an underling whom he supervised. In determining whether someone is a supervisor or manager for section 848 purposes, we must heed the ordinary meanings of these terms. See United States v. Wilkinson, 754 F.2d 1427, 1431 (2d Cir.), cert. denied, Shipp v. United States, — U.S. -, 105 S.Ct. 3482, 87 L.Ed.2d 617 (1985); United States v. Mannino, 635 F.2d 110, 117 (2d Cir.1980). In ordinary parlance, a relationship of supervision is created when one person gives orders or directions to another person who carries them out. In light of the dominant position of Richard Stratton in the overall scheme, the jury was entitled to infer that, in making drug-related payments, Gabrielle Stratton was acting at her husband’s direction.
Michelle Siegel acted as a conduit between Hammoud and Gabrielle Stratton in connection with the Canadian money transfers. Stratton disputes his supervision of Siegel, claiming that the evidence does not demonstrate that she was a knowing participant in the drug scheme. However, Gabrielle Stratton made the last of her payments to Hammoud, in the amount of $212,000, in Siegel’s presence, at which time Siegel heard Gabrielle Stratton tell Hammoud that there would be no future drug payments. From this evidence, the jury was entitled to infer that Siegel was a knowing participant in the conspiracy and that Richard Stratton was the source of her instructions to act as intermediary between Hammoud and Gabrielle Stratton.
Stratton was also in a managerial role with regard to the Parnesses. He “organized” them by bringing them into the conspiracy to provide trucking and storage services and to provide a buyer of dates as a cover for the drug shipment. He “supervised” or “managed” them by assigning *828Leonard Parness the role of picking up the hashish and by giving instructions regarding disposition of the stored hashish. Stratton presided over the division of profits among the conspirators, and Steven Parness clearly acquiesced in his subordinate position when he allowed Stratton to pay Berro $30,000 over his objection and to state that the Parnesses would have no share of the profits from the hashish oil. Although Stratton argues that the Parness-es were independent rather than subordinate actors, the jury was entitled to draw a contrary conclusion. Therefore, the evidence is sufficient to establish that Strat-ton supervised at least six people in connection with his drug scheme.
B. The Parnesses
Leonard and Steven Parness contend that the evidence was insufficient to support their convictions for conspiring to import, and importing, hashish. However, the Government’s proof, given largely by co-conspirator Hammoud, described the Parnesses’ role in providing a cover for the hashish shipment and in transporting and storing the hashish. The Parnesses argue in essence that the jury should not have believed Hammoud. However, an appellate court will not second-guess a jury’s finding on credibility. See, e.g., United States v. Taylor, 464 F.2d 240, 243 (2d Cir.1972). The Parnesses also argue that their innocence is proved by the failure of Customs officials to find the hashish hidden in the cargo of dates. Since, on appeal, all permissible inferences must be drawn in the Government’s favor, see, e.g., United States v. Young, supra, 745 F.2d at 762, this argument must be rejected as merely an attempt to substitute the defendants’ view of the evidence for the jury’s.
IV. Evidentiary Rulings
Three of Bernard Farbar’s conversations with Hammoud and Agent Maguire were successfully recorded and admitted into evidence. During these conversations, Far-bar described his attempts to locate the last ton of hashish stored by the Parnesses and outlined the general history of the drug conspiracy. In so doing, Farbar inculpated himself and the other appellants. Farbar’s statements are admissible against him as admissions of a party opponent. Fed.R. Evid. 801(d)(2). Stratton and the Parnesses contend that the trial court erred in admitting Farbar’s hearsay statements against them. We agree with the Government that Farbar’s statements are admissible against Stratton and the Parnesses as declarations against interest, Fed.R.Evid. 804(b)(3), and as statements of a co-conspirator, Fed.R. Evid. 801(d)(2)(E).
A declaration against interest is not excludable as hearsay if three conditions are met: (1) the declarant is unavailable as a witness; (2) the statement is sufficiently contrary to the declarant’s pecuniary or penal interests that a reasonable person in his position would not have made the statement unless he believed it to be true; and (3) corroborating circumstances indicate that the statement is trustworthy.7 See United States v. Katsougrakis, 715 F.2d 769, 775 (2d Cir.1983), cert. denied, 464 U.S. 1040, 104 S.Ct. 704, 79 L.Ed.2d 169 (1984). Since Farbar was a defendant, he could not be called by the Government as a witness and was therefore “unavailable.” See United States v. Lieberman, 637 F.2d 95, 103 (2d Cir.1980). Hammoud, a co-conspirator, provided ample corroboration of Farbar’s taped statements through his own testimony. The only issue, therefore, is whether Farbar’s statements were sufficiently against his penal interests that a reasonable person in his position would not have made them unless true.
Farbar’s statements were overwhelmingly contrary to his penal interests. He described the history of the conspiracy, in-*829eluding Leonard Parness’ reluctance to pick up the shipment, the storage of the hashish at the house on Staten Island, and Stratton’s division of the profits among the co-conspirators. Farbar’s statements clearly tied him to the illegal scheme. Moreover, the context in which the statements were made warrants a finding of reliability. Farbar believed he was talking to co-conspirators rather than the authorities. He therefore had no reason to lie or attempt to curry favor. Compare id. with United States v. Bailey, 581 F.2d 341 (3d Cir.1978).
Stratton and the Parnesses argue that Farbar had a motive to lie, which makes his statements unreliable and inadmissible. They argue that Farbar told Hammoud and Maguire that he was doing his best to locate and sell the additional ton of hashish so that Nassif Berro would not cooperate with the authorities. Initially, we note that the statement is generally inculpatory. By indicating that he knows that the Parness-es were last in possession of the hashish and that he has some influence over them, Farbar has suggested his complicity in the drug scheme. Moreover, Farbar’s gratuitous comments about the prior course of the drug conspiracy strengthen the reliability of this statement. While Farbar may have lied when he said he tried his best to help Nassif Berro, the trial judge was entitled to credit, for purposes of admissibility, his statements relating to the drug conspiracy. Chief Judge Motley did not err in finding sufficient reliability to justify admission under Fed.R.Evid. 804(b)(3).
Farbar’s statements are also admissible against Stratton and the Par-nesses as admissions “by a co-conspirator ... during the course of and in furtherance of the conspiracy.” Fed.R.Evid. 801(d)(2)(E). Farbar’s statements were made in furtherance of the conspiracy to distribute hashish.8 He told Hammoud that he would attempt to locate the additional hashish for sale. Stratton argues that the statements cannot be used against him because he was not charged with being a member of this conspiracy. Although the conspiracy to distribute count was severed prior to trial as to Stratton, it is not necessary that the Government charge a conspiracy to take advantage of Fed.R. Evid. 801(d)(2)(E). The Government merely needs to demonstrate that the declarant and the defendants against whom the statements are offered are members of a conspiracy in furtherance of which the statements are made, see United States v. Barnes, 604 F.2d 121, 156 (2d Cir.1979), cert. denied, 446 U.S. 907, 100 S.Ct. 1833, 64 L.Ed.2d 260 (1980), and that this conspiracy is “factually intertwined” with the offenses being tried, United States v. Lyles, 593 F.2d 182, 194 (2d Cir.), cert. denied, 440 U.S. 972, 99 S.Ct. 1537, 59 L.Ed.2d 789 (1979). The Parnesses argue that they had withdrawn from the conspiracy to distribute hashish at the time Farbar made his statements but offer no evidence of an affirmative act of withdrawal.
Stratton and the Parnesses claim that, even if Farbar’s statements otherwise qualify, they should have been excluded because Farbar lacked personal knowledge of some of the events recited. For example, Farbar says that Stratton told him that he (Stratton) had threatened Hammoud’s family. However, appellants misconceive the nature of the personal knowledge requirement, see Fed.R.Evid. 602, in the hearsay context. When A testifies that B told him of an event, A usually has personal knowledge only of B’s report. It is B who has personal knowledge of the event. Thus, the hearsay rules require that the declarant, B in our example, have personal knowledge of the events recounted, not that the witness have such personal knowledge. See United States v. Lang, 589 F.2d 92, 98 (2d Cir.1978). Thus, Farbar could have testified to Stratton’s report of the *830threats because the threats were within the personal knowledge of Stratton. Nor is there a hearsay-within-hearsay problem. Stratton’s threats are not hearsay because not offered for their truth; the threats are verbal acts. Stratton’s report of the threats to Farbar, his chief assistant, is not hearsay because it is a statement of a co-conspirator in furtherance of the conspiracy, Fed.R.Evid. 801(d)(2)(E); therefore Farbar could have testified to Stratton’s report of the threats. Finally, tapes may be used instead of Farbar’s live words because, as discussed above, Farbar’s statements are declarations against interest and themselves also those of a co-conspirator in furtherance of the conspiracy.
Stratton and the Parnesses also argue that the admission of Farbar’s statements against them violates their Sixth Amendment right to confrontation. Though a hearsay exception does not end the Confrontation Clause analysis, see, e.g., California v. Green, 399 U.S. 149, 155-56, 90 S.Ct. 1930, 1933-34, 26 L.Ed.2d 489 (1970), a finding of reliability sufficient to admit a statement against penal interest will normally satisfy Sixth Amendment concerns. Cf. Dutton v. Evans, 400 U.S. 74, 89, 91 S.Ct. 210, 219, 27 L.Ed.2d 213 (1970) (giving weight, for Sixth Amendment purposes, to fact that co-conspirator’s statement was against his penal interest). Moreover, although a higher standard of reliability is imposed if the hearsay statements are “crucial” to the Government’s case, id., Farbar’s statements were not of this nature. His description of the drug conspiracy was largely repetitive of Ham-moud’s live testimony, which was subject to cross-examination.
Appellants make two other claims. First, they argue that, even if Farbar's statements were admissible, Hammoud’s statements from the tapes should not have been admitted for their truth. This Court has held that such recorded statements are admissible to provide the context for the declarant’s admissions. See United States v. Murray, 618 F.2d 892, 900 (2d Cir.1980). Appellants would have been entitled to a limiting instruction preventing the jury from considering Hammoud’s assertions for their truth had such an instruction been requested. See id. In the absence of such a request, the appellants cannot challenge admission of Hammoud’s statements. Second, Stratton challenges the admission of his threat against Hammoud’s family as unduly prejudicial under Fed.R.Evid. 403. However, threat evidence was relevant to establish Stratton’s supervisory role concerning Hammoud, see United States v. Thomas, 632 F.2d 837, 844 (10th Cir.), cert. denied, 449 U.S. 960, 101 S.Ct. 373, 66 L.Ed.2d 227 (1980), and the trial court was within its discretion in finding that the Rule 403 balance favored admission.
V. The Jury Verdict
All appellants contend that the trial court erred in accepting the verdict of eleven jurors. On Monday, October 8, 1984, after summations had begun but prior to the commencement of deliberations, Juror No. 10 informed the district judge that she would have to leave at noon on Wednesday to observe the Jewish holiday of Succoth, which would last through Thursday and Friday. The trial court discussed the situation with counsel and suggested that an alternate be substituted before deliberations began. Defense counsel, apparently perceiving Juror No. 10 to be more favorable to their cause than Alternate No. 1, objected to substitution. The trial judge heeded this objection and allowed Juror No. 10 to continue.9 Deliberations began on Tuesday, October 9, and continued throughout the following morning. At *831noontime Juror No. 10 insisted on leaving. The trial judge then decided to excuse the juror and continue with eleven jurors, rejecting defendants’ request to adjourn for 4V2 days until all twelve jurors could return the following Monday. Later in the day, the remaining eleven jurors, after further deliberations, returned unanimous verdicts of guilty.
A twelve-member jury was once thought to be a constitutional requirement in federal criminal trials, see Thompson v. Utah, 170 U.S. 343, 18 S.Ct. 620, 42 L.Ed. 1061 (1898), but the Supreme Court has more recently made clear that the Constitution does not require twelve jurors for conviction, Williams v. Florida, 399 U.S. 78, 90 S.Ct. 1893, 26 L.Ed.2d 446 (1970). In construing the Sixth Amendment right to a jury trial, applicable to the states through the Fourteenth Amendment, see Duncan v. Louisiana, 391 U.S. 145, 88 S.Ct. 1444, 20 L.Ed.2d 491 (1968), Williams held that a six-member jury was constitutionally sufficient.10 The Court explicitly observed that the considerations bearing on the desirability of a twelve-member jury in federal criminal trials were left “to Congress.” Id., 399 U.S. at 103, 90 S.Ct. at 1907. Since Congress may legislate as to jury size, the Supreme Court may prescribe by rule, pursuant to the Enabling Act, 18 U.S.C. §§ 3771, 3772 (1982), that under certain circumstances a trial judge may excuse a juror and accept a verdict of eleven jurors.
The Supreme Court did so in 1983 when it amended Fed.R.Crim.P. 23(b) to provide:
Juries shall be of 12 but ... if the court finds it necessary to excuse a juror for just cause after the jury has retired to consider its verdict, in the discretion of the court a valid verdict may be returned by the remaining 11 jurors.
Prior to amendment, Rule 23(b) permitted a verdict of fewer than twelve jurors only by stipulation. The amended rule was prompted by the dilemma posed by such cases as United States v. Meinster, 484 F.Supp. 442 (S.D.Fla.1980) (juror had heart attack during jury deliberations after four months of trial), aff'd, 664 F.2d 971 (5th Cir.1981), and United States v. Barone, 83 F.R.D. 565 (S.D.Fla.1979) (juror became incapacitated for psychiatric reasons during jury deliberations after six months of trial). In such cases, the trial judge either had to empanel an alternate juror or had to declare a mistrial despite a substantial expenditure of public resources. To avoid a mistrial, the trial judge in Meinster and Barone substituted an alternate juror. The technique of substituting an alternate after deliberations have begun was approved by this Court, in limited circumstances, in United States v. Hillard, 701 F.2d 1052 (2d Cir.), cert. denied, 461 U.S. 958, 103 S.Ct. 2431, 77 L.Ed.2d 1318 (1983). However, this technique poses problems. Even though the jurors will be instructed to disregard previous deliberations upon empaneling of an alternate, they may not be able to nullify the effect of past discussions. Moreover, Fed.R.Crim.P. 24(c) seems to require the dismissal of alternate jurors once deliberations have begun. United States v. Hayutin, 398 F.2d 944, 950 (2d Cir.), cert. denied, 393 U.S. 961, 89 S.Ct. 400, 21 L.Ed.2d. 374 (1968); see United States v. Hillard, supra, 701 F.2d at 1058. In allowing the court to accept an eleven-juror verdict, Rule 23(b) was designed to provide a preferred mechanism for avoiding a mistrial. See Fed.R.Crim.P. 23(b), advisory committee note. Indeed, Hillard questioned whether substituting an alternate during deliberations would be *832condoned after the amendment to Rule 23(b) becomes effective. 701 F.2d at 1061.
We do not agree with appellants that Rule 23(b) is to be used only where a juror suffers permanent or at least lengthy incapacitation. We read the “just cause” standard more broadly to encompass a variety of temporary problems that may arise during jury deliberations, confronting the trial judge with the need to exercise sound discretion as to the procedure to be followed at a particularly sensitive stage of the trial. The appellants suggest that it was not “necessary to excuse [Juror No. 10] for just cause” since her absence due to religious observance would have lasted only 4V2 days. However, the trial judge was entitled to conclude that an adjournment of 4V2 days would be less desirable than an eleven-juror verdict. Adjournment would have risked dulling the jurors’ recollections of the evidence and summations and heightened the danger that the. jurors would discuss the case with outside persons. We note that the record does not present even the slightest basis to believe that Juror No. 10 was excused on a pretext to remove an obstacle to reaching a unanimous verdict. Under the circumstances of this case, the trial judge did not abuse her discretion in accepting an eleven-juror verdict.
Our view is confirmed by the few decisions that have considered Rule 23(b). In United States v. Hilliard, supra, a juror became ill after 2V2 days of deliberations followed by a three-day recess. The trial judge refused to accept the suggestion that he order a one-day adjournment to see if the ill juror recovered. Instead, fearful of the hazards of further delay, the trial court empaneled an alternate with the subsequent approval of this Court. Compared to the risks accepted in Hilliard, the decision here to accept an eleven-juror verdict was the more prudent course.
A similar problem was presented in United States v. Gambino, 598 F.Supp. 646 (D.N.J.1984), the only reported decision to interpret amended Rule 23(b). In Gambi-no, the Assistant United States Attorney trying the case accidentally put three pieces of paper containing her notes into the exhibit box. Two of the papers were innocuous. The third, which was seen by one of the jurors, contained comments about the defendant. Judge Lacey, a member of the Supreme Court Advisory Committee on the Federal Rules of Criminal Procedure, determined that the prejudice resulting from the juror’s viewing the prosecutor’s notes outweighed any prejudice that might result from proceeding with eleven jurors.
Nor are Dunkerley v. Hogan, 579 F.2d 141 (2d Cir.1978), cert. denied, 439 U.S. 1090, 99 S.Ct. 872, 59 L.Ed.2d 56 (1979), and United States v. Essex, 734 F.2d 832 (D.C.Cir.1984), relied upon by appellants, to the contrary. In Dunkerley, this Court held that the Double Jeopardy Clause prevented retrial of a defendant where the trial judge in the first trial declared a mistrial, over the defendant’s objection, instead of granting a seven-to-ten-day adjournment to allow the defendant to recover from a collapsed lung and attend the trial. Dunkerley merely notes that it was error to declare a mistrial where adjournment was available. The trial court had no third choice.
In United States v. Essex, supra, which arose under the prior version of Rule 23(b), unusual circumstances caused the trial to begin without any alternate jurors.11 The trial judge decided to proceed after the defendant stipulated to accept the verdict of eleven jurors if something happened to one of the remaining twelve. Rule 23(b), both before and after amendment, provides:
Juries shall be of 12 but ... the parties may stipulate ... that a valid verdict may be returned by a jury of less than 12 should the court find it necessary to excuse one or more jurors for any just *833 cause after trial commences, added.] [Emphasis
Deliberations began on a Friday and were adjourned until the following Monday. On that Monday, only eleven of the twelve jurors returned. Without making any investigation to determine the reason for the missing juror’s absence, the trial judge decided to proceed with eleven jurors. The D.C. Circuit reversed because there was nothing in the record upon which a finding of “just cause” could be based. See United States v. Essex, supra, 734 F.2d at 842. In the instant case, the trial court, using the discretion granted by the amended rule in the absence of a stipulation, has articulated sufficient reason to excuse a juror during deliberations. See United States v. Hilliard, supra, 701 F.2d at 1055.
Though not raised by appellants, we think consideration should be given to the arguable contention that, even if amended Rule 23(b) accorded the trial judge a discretion that was not abused in this case, the provisions of the amended rule could not validly be applied in a trial for conduct occurring prior to the promulgation of the amended rule.12 The Ex Post Facto Clause of the Constitution, Art. I, § 9, cl. 3, operates primarily to bar the retroactive application of legislative changes that define criminal offenses or enhance criminal penalties. See Weaver v. Graham, 450 U.S. 24, 28, 101 S.Ct. 960, 963, 67 L.Ed.2d 17 (1981). However, the Clause has also been applied to some procedural changes. See, e.g., Thompson v. Utah, supra (state law reducing number of jurors from twelve to eight); Kring v. Missouri, 17 Otto 221, 107 U.S. 221, 2 S.Ct. 27, 443 L.Ed. 506 (1883) (state law specifying that conviction for lesser included offense is no longer deemed an acquittal of greater offense); United States v. Henson, 486 F.2d 1292 (D.C.Cir.1973) (in banc) (federal law eliminating discretion of trial judge to exclude prior convictions to impeach credibility of witness, including defendant). On the other hand, the Clause has been held inapplicable to numerous other changes in criminal procedure. See, e.g., Beazell v. Ohio, 269 U.S. 167, 46 S.Ct. 68, 70 L.Ed. 216 (1925) (limiting right to severance of co-defendants); Mallett v. North Carolina, 181 U.S. 589, 21 S.Ct. 730, 45 L.Ed. 1015 (1901) (granting state a right of appeal); Thompson v. Missouri, 171 U.S. 380, 18 S.Ct. 922, 43 L.Ed. 204 (1898) (broadening standards for authenticating and introducing handwriting examplars); Gibson v. Mississippi, 162 U.S. 565, 16 S.Ct. 904, 40 L.Ed. 1075 (1896) (change in grand jury selection procedure); Duncan v. Missouri, 152 U.S. 377, 14 S.Ct. 570, 38 L.Ed. 485 (1894) (reducing number of judges hearing defendant’s appeal); Hopt v. Utah, 110 U.S. 574, 4 S.Ct. 202, 28 L.Ed. 262 (1884) (enlarging class of competent witnesses). The principle that identifies those few procedural changes to which the Ex Post Facto Clause applies is not readily apparent.13 It has been said that the Clause applies to those changes that impair the “substantial rights” of a criminal defendant, see, e.g., Kring v. Missouri, supra, 107 U.S. at 232, 2 S.Ct. at 452; United States v. Henson, supra, 486 F.2d at 1306, though the meaning of “substantial” in this context is not clear.
In this case, the starting point for our analysis must be Thompson v. Utah, supra. The defendant in Thompson had initially been tried in federal court, with a jury of twelve, for crimes committed in a federal territory. After the defendant prevailed on a new trial motion, the territory became the State of Utah. The subsequent state trial was conducted with a jury of eight, pursuant to Utah law. The Supreme Court held that the defendant’s second conviction violated the Ex Post Facto Clause by denying him a substantial procedural right that was guaranteed by the Sixth *834Amendment at the time of his conduct — the right to a jury of twelve.
However, the major premise of Thompson has been undercut by Williams v. Florida, supra, in which the Court held that neither the Sixth nor Fourteenth Amendment guarantees a jury of twelve. The Court noted that a jury of six was constitutional because it contained the essential elements of a jury:
To be sure, the number should be large enough to promote group deliberation, free from outside attempts at intimidation, and to provide fair possibility for obtaining a representative cross-section of the community. But we find little reason to think that these goals are in any meaningful sense less likely to be achieved when the jury numbers six, than when it numbers 12 — particularly if the requirement of unanimity is retained.
Id., 399 U.S. at 100, 90 S.Ct. at 1905. Thus, Williams suggests that the absolute right to a jury of twelve that appellants possessed prior to the 1983 amendment of Rule 23(b) is no longer viewed as a “substantial right” by the Supreme Court.14
In light of Williams, we hold that retroactive application of amended Rule 23(b), allowing conviction by eleven jurors, is not an Ex Post Facto violation. See State v. McIntosh, 23 Ariz.App. 246, 532 P.2d 188 (1975) (approving retroactive change to fewer than twelve jurors); State v. Maresca, 173 Conn. 450, 377 A.2d 1330 (1977) (same); Iseton v. State, 472 N.E.2d 643 (Ind.App.1984) (same). But see McSears v. State, 247 Ga. 48, 273 S.E.2d 847 (1981). It is highly unlikely that retroactive application of the amended rule will seriously disadvantage the defendant. No empirical data has been located comparing the results of criminal trials with twelve jurors to those obtained with eleven jurors. Some data, mostly probability studies, indicate, with internal contradictions, that a defendant may face a slight disadvantage in some respects when the jury size drops from twelve to six, but also indicate that a decrease in jury size of only one person may have only the most minute effect.15 *835Whatever disadvantage to the defendant may occur from reducing the jury size from twelve to eleven is of insufficient proportion to give him a constitutional right to a jury of twelve, Williams v. Florida, supra, 399 U.S. at 101, 90 S.Ct. at 1906, and does not affect the substantial rights of the defendant for Ex Post Facto purposes. See Iseton v. State, supra.
VI. Summary Contempt
Appellant Stratton appeals his summary contempt citation, contending that it was improper under Fed.R.Crim.P. 42(a). On a number of occasions throughout the trial, Stratton, who represented himself, attempted to apprise the jury of his fifteen-year sentence for conviction on drug charges in the District of Maine. Each time, the trial judge informed him that the Maine ease was not relevant to the present charges. Just prior to the summations, the district judge warned Stratton not to appeal for sympathy on the basis of the Maine conviction. Nevertheless, in his summation Stratton told the jury:
Whatever your verdict, however you decide the final chapter of this book, remember that even as you do what I believe you will do and write “not guilty,” Richard Stratton does not walk out of this courtroom a free man. Richard Stratton will go back to prison to serve out the rest of his fifteen-year sentence.
The trial judge interrupted Stratton’s summation and struck this remark. Stratton then made one more statement to conclude his summation. The District Court excused the jury and held Stratton in contempt of court for flagrant violation of its instructions. At the end of the day, the Court sentenced Stratton to six months’ imprisonment pursuant to Rule 42(a) and made written findings in support of the contempt citation.
Rule 42(a) states:
A criminal contempt may be punished summarily if the judge certifies that he saw or heard the conduct constituting the contempt and that it was committed in the actual presence of the court. The order of contempt shall recite the facts and shall be signed by the judge and entered of record.
If summary contempt as provided in Rule 42(a) is improper, contempt can be punished only pursuant to Rule 42(b), which incorporates full due process protections. Although Rule 42(a) seems to suggest that summary contempt is permissible whenever the trial judge witnesses the contemptuous conduct, the rule has been given a more limited scope. The summary contempt power may be used only when necessary to preserve the authority of the court. See United States v. Wilson, 421 U.S. 309, 318, 95 S.Ct. 1802, 1807, 44 L.Ed.2d 186 (1975); Johnson v. Mississippi, 403 U.S. 212, 91 S.Ct. 1778, 29 L.Ed.2d 423 (1971); United States v. Martin-Trigona, 759 F.2d 1017 (2d Cir.1985). Stratton argues that it was unnecessary for the trial court to punish him summarily because he had finished his summation by the time he was cited for contempt. He also argues that the trial court’s delay in sentencing him is further evidence of the lack of necessity.
The facts of the pending case fall between two patterns that have previously been considered. Sometimes, contemptuous conduct occurring in the presence of the court is adjudicated and punished immediately upon its occurrence. E.g., United States v. Wilson, supra; United States v. Martin-Trigona, supra. In other instances, the only immediate action is a citation for contempt, and final adjudication *836and punishment is deferred until the conclusion of the trial, Taylor v. Hayes, 418 U.S. 488, 94 S.Ct. 2697, 41 L.Ed.2d 897 (1974); United States v. Lumumba, 741 F.2d 12 (2d Cir.1984). Where punishment is deferred until after trial, summary procedure may not be used. Taylor v. Hayes, supra; United States v. Lumumba, supra. In the instant case, the contemnor was held in contempt within moments of his contemptuous conduct, and the contempt sentence was imposed at the end of the day, prior to the conclusion of the trial.
We do not believe that the procedure used by the trial judge demonstrated a lack of necessity for vindication of the court’s authority by use of the summary contempt power. Though Stratton had finished his summation, the trial had not ended, and further occasions could arise when Stratton might be tempted to flout the trial judge’s authority, for example, during the summations of other counsel or during the jury charge. The trial judge was entitled to use an effective sanction to deter Strat-ton from again disregarding her instructions. The momentary delay from the occurrence of the contempt until the contempt citation resulted from the trial judge’s forbearance in permitting Stratton to conclude his summation without the interruption of a summary contempt proceeding and her sensible decision to excuse the jurors rather than conduct the proceeding in their presence. This momentary delay indicated only admirable restraint by the trial judge to minimize the risks of adverse effects of the contempt citation upon the conduct of the trial.
Nor does the further brief delay in sentencing until the end of the day indicate that summary contempt was unnecessary. Rather, it reflects the careful restraint of an experienced trial judge who preferred not to select a contempt sentence until the end of the trial day. Unlike Taylor and Lumumba, where sentencing imposed after trial could have had no prophylactic effect upon the contemnor, the trial judge here imposed a sentence at a point where it retained a deterrent effect for the remainder of the trial. The judge selected an appropriate time — after the confrontation of the episode had subsided and before the contemnor had much opportunity to misbehave again. Use of the summary contempt procedure was not precluded by the trial judge’s decision not to impose sentence the instant her authority was challenged.
VII. Conclusion
The judgments of the District Court are affirmed.16