Appellant Richard Ramos Algarin, an attorney, was convicted on eleven counts of conspiracy and other offenses relating to immigration fraud perpetrated through sham marriages between aliens and United States citizens. One of the several witnesses testifying against him was Jose Maria Algarin Rivera, an indicted coconspirator1 and former employee. When Jose Maria testified, the prosecution introduced and read to the jury an agreement between Jose Maria and the Government providing that he would plead guilty to one of the four counts lodged against him and would cooperate with the Government. In return, the Government would dismiss the remaining three counts and “make no recommendations to the Court with regard to punishment” of Jose Maria.
The day after the jury rendered the verdict against appellant, the Government successfully moved to dismiss all charges *564against Jose Maria. In support of its motion it said that Jose Maria had cooperated fully with the Government, both before and during the trial and despite threats to his well-being. In oral argument before this court, the Government further explained that it decided suddenly, after the end of appellant’s protracted (seven day) trial, that Jose Maria was a figure of minimal importance who was not worth the effort to punish on one count as originally intended. The government attorneys had travelled to Puerto Rico from Washington and, allegedly, they had “had enough” and wanted to go home without delay. Appellant contends, nonetheless, that, as a matter of due process, the suspicious sequence of events entitles him to a new trial, or at least to an evidentiary hearing on the question of whether the Government had covertly agreed before the verdict in appellant’s case to dismiss all charges against Jose Maria.2
The Supreme Court’s decision in Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), is the controlling authority. In that case, an unindicted cocon-spirator who testified against Giglio provided the only testimony linking him with the crime. The Government’s case “depended almost entirely on [the coconspirator’s] testimony; without it there could have been no indictment and no evidence to carry the case to the jury.” Id. at 154, 92 S.Ct. at 766. The coconspirator’s credibility was therefore a controlling issue. The prosecution created the impression that the witness had received no promises of lenity, but after trial the defense uncovered evidence forcefully indicating that an undisclosed promise of immunity had been made to the coconspirator prior to trial. The Court ruled that due process required that Giglio be retried and held that, “When the ‘reliability of a given witness may well be determinative of guilt or innocence’, nondisclosure of evidence affecting credibility falls within [the Brady rule requiring a new trial regardless of the prosecution’s good or bad faith.]” Id., quoting Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959); see Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194,10 L.Ed.2d 215 (1963). “A finding of materiality of the evidence is required under Brady, supra at 87 [83 S.Ct. 1196, 10 L.Ed.2d 215]. A new trial is required if ‘the false testimony could . in any reasonable likelihood have affected the judgment of the jury . . . .” Gig-lio, supra, 405 U.S. at 154, 92 S.Ct. at 766, quoting Napue, supra, 360 U.S. at 271, 79 S.Ct. 1173.
This court has construed Giglio to require a two-part showing by one seeking retrial because of an undisclosed plea bargain. United States v. Bynum, 567 F.2d 1167 (1st Cir. 1978). First, the defendant must show that there was a promise of aid made by the Government to a key witness that was not disclosed to the jury. Second, he must demonstrate that, in the language of Giglio and Napue, “the false testimony could ... in any reasonable likelihood have affected the judgment of the jury. . . . ” Id. at 1168-69; cf. United States v. Street, 570 F.2d 1, 4 (1st Cir. 1977).
Applying this two-part test in the present case, we are unable to say that the first part has as yet been established, although the Government’s failure to implement the plea agreement does give ground for suspicion that an undisclosed promise may have been made. The Government vehemently denies any deal with Jose Maria other than that contained in the plea agreement, explaining the dismissal as an abrupt unilateral change of mind made after conclusion of appellant’s trial. If the Government is telling the truth, there would be no impropriety since the witness’ testimony could not have been affected by any undisclosed *565promise of aid. On the other hand, the Government’s sudden about-face is troubling. If in fact it had a prior understanding with the witness which went beyond the plea agreement, its conduct here would not only come within Giglio but would amount to serious misconduct. See ABA Project on Standards for Criminal Justice, The Prosecution Function and the Defense Function § 3.11(a), (b). See generally United States v. Agurs, 427 U.S. 97, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976); Ramos Colon v. United States Attorney, 576 F.2d 1 (1st Cir. 1978).
Given the circumstances, we would be reluctant to let matters stand without further inquiry were it not for the fact that appellant totally fails to establish that he comes within part two of the Giglio standard. Under this part of the test, the court must determine whether the false testimony could in any reasonable likelihood have affected the judgment of the jury. Here even assuming the worst — i. e. that there was a secret pre-verdict understanding between the Government and witness to dismiss all, rather than only three of four, counts — we are unpersuaded that disclosure of this could reasonably have affected the judgment of the jury on the issue of guilt or innocence. Even Government misconduct does not warrant reversal if it is harmless.3 See Ramos Colon v. United States Attorney, supra, 576 F.2d at 4; United States v. Bourque, 541 F.2d 290, 292-93 (1st Cir. 1976). The possible prejudice from the improper conduct must be weighed against the effect of the properly admitted evidence. See Morgan v. Hall, 569 F.2d 1161, 1166 (1st Cir. 1978), cert. denied, -U.S. -, 98 S.Ct. 3103, 57 L.Ed.2d 1142 (1978).
The Government’s case against appellant can only be considered overwhelming. He was accused of arranging, for a fee, a series of “marriages between aliens and United States citizens in order to procure permanent residency status for the aliens. Counts one through four of the indictment4 charged appellant with arranging the formalities of a “divorce” between one Roman Acosta Acosta and his wife of twenty years, Dominga Vargas, citizens of the Dominican Republic. Appellant was-said to have conspired with his clients and with Jose Maria, his employee, to do this and to set up his clients’ subsequent “marriages” to United States citizens Nicolas Garcia Garcia and Norma Iris Velasquez Aviles, in violation of 18 U.S.C. §§ 2, 371, 1001 and 1546. In connection with these machinations, appellant was charged in addition with conspiring to make and making misrepresentations of material facts in United States documents, in violation of 18 U.S.C. § 1001, and with selling a false birth certificate to Roman Acosta Acosta, in violation of 18 U.S.C. § 1427.
Roman Acosta Acosta, Dominga Vargas, Nicolas Garcia Garcia, and Iris Velasquez Aviles all testified on behalf of the Government. Each related how appellant had arranged the marriages (and the divorce, in the case of Acosta and Vargas); that each had been party to a marriage ceremony in which he or she wed a complete stranger introduced through appellant; and that the newly “married” couples never lived together or consummated their marriages after the ceremonies. Dominga Vargas and Roman Acosta testified that their objective in consulting appellant had been to • legalize their status in United States territories. Nicolas Garcia and Iris Aviles testified that they received individual fees for their services. From the testimony of Garcia and Vargas it emerged that the “Petition to Classify Status of Alien Relative for Issuance of Immigrant Visa”, filed by appel*566lant with the Immigration Service on their behalf, was incorrect in two material respects: it falsely indicated that Vargas was living in the Dominican Republic at the time of filing and that she and Garcia had lived together previously at what was in fact Vargas’ then current address in Puerto Rico. An INS agent .also testified about a false birth certificate provided Roman Acosta Acosta by appellant.
Evidence concerning one subsequent marriage arranged by appellant between an alien and a United States citizen was introduced, including testimony of both participants. Related offenses were charged in counts 22 and 23.5 Counts 15 through 19 dealt with two separate incidents in which noncitizens who had married citizens with the sole purpose of obtaining permanent resident alien status had sought and obtained appellant’s services in completing the formalities (such as filing the appropriate papers with INS).6
Jose Maria Algarin Rivera’s testimony touched directly on only four of these counts. He gave evidence about the details of the negotiations between appellant and Roman Acosta Acosta concerning a fee and about appellant’s dickering with Nicolas Garcia Garcia over the fee for his services in marrying Dominga Vargas. He also testified about the brief wedding ceremony between Roman Acosta and Norma Iris Velasquez Aviles and about a gathering after the ceremony — an event that was substantially irrelevant to the elements of the crimes charged against appellant. Otherwise, his testimony merely corroborated and added detail to the prior testimony of Acosta, Vargas, Garcia and Aviles. Direct and cross-examination of Jose Maria occupy 24 pages of an 836-page transcript.
Appellant’s assertion that Jose Maria was the “single most important witness” to testify distorts, in our view, the tenor of the evidence. Jose Maria’s testimony was clearly outranked in importance by the accumulated testimony of other government witnesses. Appellant claims that Jose Maria’s testimony was important because it “transcended the counts in which he was named.” Appellant relies on Jose Maria’s status as appellant’s employee, coupled with one statement in his testimony, to support this assertion. That statement, elicited on cross-examination, was as follows:
“Q. And did you ever see Mr. Ramos or hear Mr. Ramos give any special instructions as to getting a woman or a man to get married with an alien?
A. That was done daily. That was a public school.”
But quite apart from this testimony the evidence on each of the eleven counts was solid. The participants in the marriages amply demonstrated that appellant had knowingly or, at the very least, recklessly made these fraudulent arrangements. See United States v. Sarantos, 455 F.2d 877 (2d Cir. 1972). The number of similar events surrounding the marriages weakened appellant’s defense that he was taken in by his “desperate” clients; it could readily be inferred without referring to Jose Maria’s statement quoted above that appellant was not unaccustomed to making this sort of illicit arrangement.
Furthermore, Jose Maria’s credibility was already subject to close scrutiny, since it *567was revealed that he had been fired by appellant and had entered a favorable plea agreement which, while not involving dismissal of all charges, did provide for distinct benefits. Finally, Jose Maria’s testimony was not relied on heavily in closing argument, although defense counsel did seek to impeach it by emphasizing the existence of the plea agreement. We are unable to accept the argument that disclosure of an even more favorable agreement between Jose Maria and the Government would in any reasonable likelihood have affected the jury’s appraisal of appellant’s guilt.7
Pre-indictment delay
Appellant charges that a delay between commission of the offenses charged (which occurred from 1971 through 1974) and the indictment (issued in May 1976) was an “impermissible" tactic used to amass additional charges against him rather than to pursue investigative leads. His claim must be measured by the due process standard of United States v. Lovasco, under which “proof of prejudice is generally a necessary but not sufficient element of a due process claim, and . . . the due process inquiry must consider the reasons for the delay as well as the prejudice to the accused.” 431 U.S. 783, 790, 97 S.Ct. 2044, 2049, 52 L.Ed.2d 752 (1977); see United States v. Marion, 404 U.S. 307, 324, 92 S.Ct. 455, 30 L.Ed.2d 468 (1971). In Lovasco, the defendant was prejudiced because two material and directly exculpatory witnesses died in the 18 month period between investigation and indictment; both of those witnesses allegedly would have been able to offer evidence negating essential elements of the crime. Lovasco, supra, 431 U.S. at 785-88, 92 S.Ct. 2044. The Government’s ostensibly investigative reasons for the preindictment delay were, on the other hand, only sparsely documented. Nevertheless, the Court found no due process violation.
In this case, by contrast, there was no real prejudice and the delay was explained by the prosecution. Appellant asserts that he was prejudiced because “it was impossible to find associates of witnesses who might provide information relevant for purposes of impeachment [of the witnesses].” Appellant was able to impeach the Government’s case, however, by bringing out on cross-examination what drinking problems and instability existed in the client-witnesses’ backgrounds. We do not think that the possibility — speculative at best — that some undiscovered acquaintance might have provided additional information tending to impeach the client-witnesses is a showing of prejudice sufficient to support a deeper due process inquiry under Lovasco. Moreover, the Government submitted a detailed affidavit stating that the delay resulted from personnel shortages in the Puerto Rico Investigations Branch of the Immigration and Naturalization Service and from a felt need for additional evidence. The first explanation speaks for itself. Appellant disputes the second, claiming that the Government had enough evidence to prosecute the 1971-*568centered offenses well before 1976. But the Government is entitled to present the strongest possible case. A good faith delay to obtain evidence of other instances of similar wrongdoing that might indicate a scheme or bolster a claim of wrongful intent is not illegitimate. See ABA Project on Standards for Criminal Justice, The Prosecution Function and the Defense Function § 3.9. The judgment that additional evidence is needed is committed to the discretion of the prosecutor, not the court. Id.; see Lovasco, supra, 431 U.S. at 793, 92 S.Ct. 2044; United States v. Daley, 454 F.2d 505, 508 (1st Cir. 1972).
Severance
For similar reasons, we conclude that it was not improper to deny appellant’s motion to sever the counts of the indictment for separate trials. Severance is a matter of discretion for the trial court; “only a strong showing of prejudice will warrant finding an abuse thereof.” United States v. Clayton, 450 F.2d 16, 18 (1st Cir. 1971), citing Gorin v. United States, 313 F.2d 641, 646 (1st Cir. 1963), cert. denied, 379 U.S. 971, 85 S.Ct. 669, 13 L.Ed.2d 563 (1965); see Fed.R.Crim.P. 14, “Relief from Prejudicial Joinder.” Rule 8(a) of the Federal Rules of Criminal Procedure allows joinder of offenses in the same indictment “if the offenses charged . . . are of the same or similar character or are based on the same act or transaction or on two or more acts or transactions connected together or constituting parts of a common scheme or plan.” In this case, the similar schemes served to demonstrate appellant’s wrongful intent and the absence of mistake or accident. See Fed.R.Evid. 404(b). The two counts that related to the divorce and remarriages of Roman Acosta Acosta and Dominga Vargas were parts of a common scheme or plan. The trial court instructed the jury that each conspiracy was to receive separate consideration. Appellant can claim to have suffered prejudice only in receiving concurrent two-year sentences on the eleven counts. Denial of the motion to sever was not an abuse of discretion. See United States v. Clayton, supra, 450 F.2d at 18-19.
Multiplicity
Appellant also complains of multiplicity in all counts of the indictment. The only specific argument he makes, however, is that counts one and three involved one conspiracy and should have been combined in one count, since they both related to the Roman Acosta/Dominga Vargas divorce and remarriages. Even were we to accept this analysis, the appropriate remedy would be to vacate one of the two counts. See United States v. Honneus, 508 F.2d 566, 570 (1st Cir. 1974), cert. denied, 421 U.S. 948, 95 S.Ct. 1677, 44 L.Ed.2d 101 (1975). This remedy would be superfluous in this case because appellant received concurrent sentences. See United States v. Moss, 562 F.2d 155, 160-61 (2d Cir. 1977). The fact that a sentence is concurrent does not automatically bar consideration of a challenge to the conviction, Benton v. Maryland, 395 U.S. 784, 791, 89 S.Ct. 2056, 23 L.Ed.2d 707 (1969); instead, we consider the prejudice that may have resulted from imposition of the challenged sentence in the defendant’s case. See Vanetzian v. Hall, 562 F.2d 88, 90 & n. 3 (1st Cir. 1977); United States v. Moss, supra. There is no indication that appellant’s sentence was enhanced by his conviction on this allegedly multiplicious count. In fact, conviction on each of the single counts could have resulted in a sentence of five years imprisonment, but concurrent sentences of only two years were imposed on all counts. United States v. Moss, supra. Furthermore, appellant was convicted of a total of 11 counts. It is difficult to conceive how reduction of that number to 10 could later influence a parole board’s determination. Nor would the reduction prevent application of a habitual offender statute if appellant were ever to be convieted of another offense and charged under that statute. Vanetzian v. Hall, supra. Finally, to the extent that appellant objects to multiplicity in the other counts, we observe that the strength of his claim is diminished by his simultaneous argument, discussed above, that the counts are so distinct that they should have been severed.
*569 Insufficient evidence of acts within the statute of limitations
Appellant maintains that, as to counts one and three, no acts in furtherance of the alleged conspiracies were shown to have been done by appellant within the relevant five-year period of limitations. He therefore argues that the counts should have been dismissed. The trial court found, however, that a document concerning count one (a “Petition to Classify Status of Alien Relative for Issuance of Immigrant Visa”) was filed on behalf of Dominga Vargas within the five-year period. The document was prepared and notarized by appellant; its filing was the final step in an effort to obtain resident status for Vargas. This was an overt act in furtherance of a conspiracy of which appellant was shown to have been part and properly could be relied upon to bring the count within the statute of limitations. United States v. Sarantos, supra, 455 F.2d at 882-83. The fact that it was not shown that defendant filed the petition himself is irrelevant; filing by a coconspirator would suffice. See Pinkerton v. United States, 328 U.S. 640, 645-48, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946); United States v. Sarantos, supra, 455 F.2d at 883.
As to count three, it was shown that appellant obtained Roman Acosta’s divorce from Norma Iris Velasquez Aviles during the five year period. This act is fairly considered part of the entire plan to obtain resident alien status for Acosta and suffices to bring count three within the statute of limitations. United States v. Sarantos, supra, 455 F.2d at 882-83.
Evidence of the prior conviction of Jose Maria Algarin
Appellant contends that the district court abused its discretion by excluding evidence of a 32-year old conviction sustained by Jose Maria Algarin Rivera, the indicted coconspirator who testified against appellant. Fed.R.Evid. 609(b) leaves the decision whether to admit a conviction older than ten years to the discretion of a trial judge and makes advance notice to opposing counsel a prerequisite to its use. Appellant did not give such notice. We find no abuse of discretion.
Instruction on the presumption of truthfulness
Without meaning to indicate our endorsement of such an instruction, we find no reversible error in the district court’s jury instruction that a witness is generally presumed to speak truthfully. The court cautioned the jury about the dangers of accomplice testimony and discussed fully both the presumption of innocence and the Government’s burden of proving appellant guilty beyond a reasonable doubt. See Cupp v. Naughten, 414 U.S. 141, 94 S.Ct. 396, 38 L.Ed.2d 368 (1973); Varela Cartagena v. United States, 397 F.2d 278, 280 (1st Cir. 1968); compare McMillen v. United States, 386 F.2d 29, 32-33 (1st Cir. 1967), cert. denied, 390 U.S. 1031, 88 S.Ct. 1424, 20 L.Ed.2d 288 (1968). Appellant did not object to the presumption of truth instruction. Given the strength of the evidence against him, the consistent testimony of the many government witnesses, and the instructions that offset the challenged instruction, we cannot agree that it amounted to plain error. Varela Cartagena v. United States, supra, 397 F.2d at 280.
Affirmed.