OPINION OF THE COURT
ALDISERT, Circuit Judge.
The main question for decision in these consolidated appeals, in a complex criminal case involving payment of graft by one of America’s largest electrical equipment manufacturing companies to a Puerto Rican official and the laundering of payments to him through a subcontractor based in Bermuda, is whether the indictments are barred by the statute of limitations. Three corporations and three individuals appeal from judgments of conviction and sentence entered on a jury verdict finding them guilty of wire fraud, mail fraud, interstate travel in aid of racketeering, and conspiracy. We affirm the conviction of appellant Twombly, Inc. on interstate travel charges brought in a separate indictment. We reverse all convictions under counts 2, 3, and 5 of the principal indictment, which relate to conduct occurring after November 5, 1975, when appellant General Electric revealed the scheme to the Governor of Puerto Rico, because we hold that the conspiracy ended as a matter of law on that date. We also reverse appellant Robert Naples’ convictions on all counts because he withdrew from the conspiracy prior to the period of limitations. We set aside the convictions and remand for a new trial on the remaining counts 1, 4, and 7, because the defendants were denied reasonable notice and opportunity to defend against the specific factual theory on which the government based its argument that the conspiracy extended beyond the accomplishment of its principal objectives and into the period of limitations, and because we are unable to determine whether the jury’s verdict was based on an impermissible ground,
I.
The theory underlying the prosecution is that the appellants and others conspired and succeeded in obtaining a multi-million dollar power plant construction contract for [798]*798appellant General Electric by bribing a Puerto Rican public official, and that they thereby defrauded the government and people of Puerto Rico of the right to the official’s faithful and disinterested services, in violation of the federal wire and mail fraud statutes, the Travel Act, and Puerto Rican law. The appellants allegedly created and transferred a “bribe fund” through a complex series of subcontract transactions designed to conceal its source and its payment. The substantive charges set forth in the two indictments relate to conduct that allegedly furthered this conspiracy. Indictment No. 80-73, returned on March 14, 1980, charged appellant Twombly, Inc. in a single count with interstate travel in aid of racketeering in violation of the Travel Act, 18 U.S.C. § 1952. Indictment No. 80-320 was returned on September 4, 1980, charging each appellant in seven separate counts. The two indictments were consolidated for trial. Twombly, Inc. was convicted of the Travel Act offense charged in indictment No. 80-73. Each defendant was acquitted on count 6 of indictment No. 80-320; and each was found guilty of wire fraud, in violation of 18 U.S.C. § 1343 (counts 1 and 2); mail fraud, in violation of 18 U.S.C. § 1341 (count 3); interstate travel in aid of racketeering, § 1952 (counts 4 and 5); and conspiracy, under 18 U.S.C. § 371 (count 7). Each defendant has appealed, and we ordered the appeals consolidated for briefing and oral argument.
The various contentions presented by the several defendants require us to consider whether the prosecution was time-barred as to some or all charges; whether Puerto Rico is a “State” as contemplated in the Travel Act, 18 U.S.C. § 1952; whether the government abused the grand jury process or evidentiary standards in obtaining the indictments; whether there was sufficient evidence to support the convictions of Schenectady Turbine Services, GE, and Twombly, Inc.; whether admission of Bermuda bank records, videotaped depositions, and the past-recolleetion-recorded testimony of witness Frank Ayer was impermissible; and whether a new trial should be granted because a mid-trial shift in the government’s theory of the continuance of the conspiracy denied appellants reasonable notice and a fair opportunity to defend against the government’s allegations.
II.
We begin by setting forth generally the facts underlying the prosecution, crediting all testimony in support of the judgment and indulging in all reasonable inferences favorable to the prosecution.
A.
In the spring of 1973, the Puerto Rico Water Resources Authority (PRWRA) invited a number of companies, including appellant GE, to submit bids for the construction of a large steam and gas turbine (STAG) power plant in Aguirre, Puerto Rico. The bid invitation required compliance with certain basic specifications, but it permitted substantial differences among the competing proposals. The Authority’s evaluation of the competing bids was, therefore, necessarily complex and somewhat subjective.1
In June 1973, several high-level employees of GE’s Gas Turbine Division, including appellant Robert Naples, met to discuss bidding strategy. They agreed that GE would bid both as a prime contractor and as a turbine equipment subcontractor for another prime bidder, Hitachi America, Ltd.
Sometime during the summer of 1973, Richard Kask, an employee in GE’s International Sales Division, met with former GE employee Vernon Twombly, the principal owner of appellant Twombly, Inc., which previously had done business in Puerto Rico. Kask said that he believed GE would need assistance in getting the contract, and [799]*799Twombly indicated that he might be able to assist. Following that conversation, Twombly called appellant Charles Mothon, another former GE employee who was then a marketing representative for Hitachi. Twombly reported Kask’s opinion that “help was needed” on the STAG contract, and he suggested that he and Mothon could work together. Mothon replied that he “would have to talk to his friends and find out what was possible.” Mothon later called Twombly and indicated that he probably could help, and Twombly relayed that message to Kask. A few days later, Mothon suggested to Twombly that GE would have to pay about $1 million to “friends,” a term that Mothon and Twombly understood to refer to persons receiving money in return for aid in obtaining a contract. Mothon indicated to Twombly that his “friend” in this instance was Carlos Velazquez Toro, the Chief of Operations of the PRWRA. Twombly relayed the $1 million figure to Kask.
The bids were opened on September 17, 1973. The competitors were permitted to review each others’ bids in detail, according to the PRWRA’s usual practice. Hitachi’s bid was not competitive, eliminating GE’s chance of participating as a subcontractor and leaving GE, Westinghouse (the low bidder), and two other bidders as contenders for the prime contract.
Mothon called Bruce Boni of GE’s Gas Turbine Division, an assistant to appellant Robert Naples, a day or two after the bids were announced. Boni and Mothon discussed “what might have to be done if GE was really interested in pursuing the business,” specifically the need to pay a “special commission,” a topic familiar to both. Boni then suggested to Naples that GE employ Twombly, Inc. as a subcontractor and a conduit for payment of the bribe, if “the proper permission to go ahead” could be obtained. Boni thereafter discussed the matter with Frank Ayer of GE’s International Sales Division, and Ayer promised to explore the question with others in that division.
Naples met on September 26, 1973, with appellant Hoyt Steele, a GE Vice President and head of the International Sales Division. Naples suggested that GE should hire Twombly, Inc. as its installation subcontractor and asked Steele to “approve a payment.” Steele met the next day with several other officers of the International Sales Division. He instructed Richard Kask to advise Vernon Twombly that Twombly, Inc. would be awarded a STAG project subcontract. If “the question of additional funds [to] be made available” to Twombly arose, Kask was to offer $300,000. Kask reported this information to Twombly the same day. Twombly indicated that $300,-000 “was probably insufficient,” and Kask communicated his response to Steele. Steele thereafter authorized Kask to offer Twombly $1 million. Kask conveyed the second offer to Twombly, and Twombly to Mothon, and Mothon stated that the proposal was acceptable.
On December 3, 1973, as a result of Velazquez Toro’s manipulations of the evaluation process, the PRWRA issued a letter of intent to contract with GE for construction of the Aguirre STAG plant. A draft evaluation report prepared by PRWRA staff had recommended awarding the contract to Westinghouse, but the final report signed by the award committee found GE’s bid better by $240,000, less than Vi of one percent of GE’s adjusted bid.
The Authority thereafter decided to add a “residual fuel option”2 to the project, however, and it temporarily suspended GE’s letter of intent on January 8, 1974. GE subsequently learned that Westinghouse was prepared to submit a low bid for the additional equipment, and GE lacked Westinghouse’s capacity to fabricate some of the [800]*800necessary components or “skids”3 in its own plants. Addition of the residual fuel option thus posed a serious threat to GE’s slender advantage. GE agreed to add $250,000 to the “special commission,” however, and the Authority thereafter decided to negotiate with GE alone for the residual fuel option. GE and the PRWRA signed a contract for construction of the STAG plant on March 15, 1974.
B.
Two factors caused the GE representatives and their co-conspirators to adopt an elaborate subcontract package. First, it was necessary to transfer the “special commission” to Velazquez Toro. Second, it was necessary to conceal the bribe from GE’s staff auditors. The government contends also that the evidence would permit an inference that the conspirators adopted the subcontract package to conceal the transaction from “others who might hold them accountable, such as law enforcement officials.” The mechanism came to be known as the “scope transfer” because it involved transferring certain functions from the “scope” of the GE Gas Turbine Division to the International Sales Division, and from the scope of GE’s own operations to an outside contract. Instead of fabricating certain equipment for the STAG project in its own plants or purchasing it from fabricators at wholesale prices through its Gas Turbine Division, GE purchased the equipment at retail from Twombly, Inc. through the International Sales Division. GE thus transferred to Twombly, Inc. the profits attributable to that equipment; and Twombly, Inc. in turn transferred those profits to Mothon by purchasing the equipment from Turbo-Electric Equipment, Ltd. (TEE), a Bermuda corporation controlled by Mothon. Mothon then delivered the money to Velazquez Toro.
By the spring of 1974, GE had discovered that the margin between the wholesale and retail prices of the equipment in the scope transfer was insufficient to generate the full bribe fund. The “margin deficit” was approximately $439,000, including the $250,-000 increase in the bribe commitment that resulted from addition of the residual fuel option. GE therefore sought to generate a larger margin by “scope transferring” two sets of components of the residual fuel option, the residual and water wash skids. GE purchased those skids from Twombly, Inc., which purchased the equipment from TEE, which in turn obtained it from appellant Schenectady Turbine Sales, Ltd., another company primarily controlled by Mothon. This transfer apparently reduced the margin deficit by $101,600. Unanticipated transportation expenses pushed the total deficit to $487,800, however, but GE apparently wrote off that amount as an “initial price reduction.” See 7 App. 1648-50.
Payment on the subcontracts between GE and Twombly, Inc. and between Twombly, Inc. and TEE occurred in a series of transfers between the spring of 1974 and June 1976. Because the limitations dates on the two indictments are March 14, 1975, and September 4,1975, see 18 U.S.C. § 3282, we are concerned only with four payments. Each is the subject of substantive charges, and each is named as an overt act in furtherance of the illegal conspiracy charged in count 7 of the later indictment.
On May 28, 1975, Twombly, Inc. cabled $94,441.50 from a New Jersey bank to TEE in Bermuda for the balance due on four distillate fuel forwarding skids, which were included in the original scope transfer. Indictment No. 80-73, filed March 14, 1980, against Twombly, Inc., names this conduct as a violation of the Travel Act, 18 U.S.C. § 1952.
Twombly, Inc. cabled an identical payment on September 5,1975, for the balance due on two water wash skids. The second indictment in counts 1 and 4 charges that this conduct violated the federal wire fraud statute, 18 U.S.C. § 1343, and the Travel Act.
[801]*801Again on December 15, 1975, Twombly, Inc. cabled $70,831.12 to TEE, for the balance due on two residual fuel forwarding skids. Counts 2 and 5 similarly allege that this transfer violated §§ 1343 and 1952.
Finally, on June 27, 1976, Twombly, Inc. mailed to TEE a check for $212,490.36, the balance due on six residual fuel forwarding skids. That mailing is named in count 3 as a violation of 18 U.S.C. § 1341 (mail fraud).
The government also introduced evidence that Mothon transferred approximately $1.25 million to Velazquez Toro in Bermuda in 1974. It concedes, however, that it did not introduce sufficient evidence to permit the jury to find that Toro received any portion of the bribe within the applicable periods of limitation.
C.
In June 1975, beset by financial difficulties caused by labor problems in Puerto Rico, Twombly, Inc. asked GE to increase the value of its contract. GE agreed to consider the request and sent its employee Carl Mutch to audit Twombly, Inc.’s project records. Apparently suspecting that the transaction was tainted by impropriety, Mutch pressed Vernon Twombly for a full disclosure. Twombly, threatened by Mutch with personal financial ruin, admitted that the GE-Twombly, Inc. contracts were used to raise money for a payment to a Puerto Rican official. GE subsequently agreed to advance Twombly, Inc. an additional $2.75 million, conditioned on satisfactory completion of the STAG project, and GE thereafter carefully monitored and regulated Twombly, Inc.’s project expenditures.
Vernon Twombly’s admissions to Carl Mutch were reported promptly to GE’s top management, which ordered an internal investigation. As a result of the investigation, a GE attorney on November 5, 1975, met with the Governor of Puerto Rico and an official of the Puerto Rico Department of Justice. The attorney disclosed the essential elements of the scheme, including the identity of the alleged bribe recipient, and the Governor instructed the Department of Justice to investigate. Puerto Rican authorities notified GE in July 1976 that they had been unable to develop evidence that Velazquez Toro had received a bribe.4 Puerto Rico has not charged any person with illegal conduct arising out of the STAG contract.
III.
The foregoing demonstrates conclusively that the illegal conspiracy terminated, as a matter of law, no later than November 5, 1975, the date of GE’s disclosure to Puerto Rican law enforcement officials. The principal purposes of the conspiracy— payment of a bribe to Velazquez Toro and award of the contract to GE — were fully accomplished prior to that date. The general purpose that allegedly underlay the conspiracy and brought it within the ambit of §§ 1341 and 1343, the federal fraud statutes — to defraud the government and people of Puerto Rico of Velazquez Toro’s faithful services — could not continue after the scheme was disclosed to high-ranking Puerto Rican officials with authority to order a prosecution. Furtherance of the concealment objective, if it continued to that date, was terminated by the disclosure. Thus no conduct after that date furthered the purposes of the illegal conspiracy alleged in the indictment. The cable transfer of funds on December 15, 1975, and the mailing of funds on June 27, 1976, can hardly be said to have related to the purposes of the conspiracy when GE, the prime defendant, had made a full disclosure to the governor of Puerto Rico on November 5, 1975. The government conceded at oral argument that no distinction can be made under the facts of this case between the substantive counts (for mail fraud, wire fraud and Travel Act offenses) and the conspiracy count, and that if the overt acts did not further the conspiracy, they will not support convictions on the substantive [802]*802counts. The substantive convictions on Counts 2, 3, and 5 for conduct which occurred on those dates accordingly must be reversed.
IV.
We next consider appellants’ argument that the second indictment, returned September 4, 1980, is barred by the five-year statute of limitations, 18 U.S.C. § 3282. Appellants contend that the objectives of the conspiracy were fully accomplished prior to September 4, 1975, and therefore that the prosecution is barred; and they argue alternatively that a new trial must be ordered because the prosecutor argued facts not supported by the evidence and improperly changed theories in his rebuttal. The government contends that the payments of September 5 and December 15, 1975, and June 27, 1976, furthered the conspirators’ original scheme. We have previously held, however, that the conspiracy terminated no later than November 5, 1975, so our consideration of the government’s argument must be limited to the September 5, 1975, wire transfer from Twombly, Inc. to TEE.
The September 5 transfer was a partial payment for two water wash skids, components of the residual fuel option. Viewed in the light most favorable to the prosecution, the evidence showed that GE added this equipment to the “scope transfer” to increase Twombly, Inc.’s profits and thereby to make additional funds available to Mothon for payment to Velazquez Toro.
We perceive three theories at least potentially available under the indictment to support a finding that this payment furthered the original purposes of the conspiracy: first, that some portion of the $94,441 was actually transferred from Twombly through TEE to Velazquez Toro to fulfill the bribe commitment; second, that the payment furthered the purposes of the conspiracy by reimbursing TEE and Mothon for prior payments to Velazquez Toro; and third, that the payment from Twombly, Inc. to TEE furthered the conspirators’ plan to conceal their conduct. The first of these theories must be eliminated, however, because the government concedes that its 'evidence would not support a finding that Velazquez Toro received any portion of the bribe during the period of limitations. It defends the judgment on the grounds that the September 5 transfer furthered the concealment purpose of the original conspiracy and that it was a reimbursement for earlier bribe payments from Mothon to Velazquez Toro.
We will require a new trial for several reasons. We need not decide whether any of the following factors alone would warrant a new trial. We are persuaded that in the circumstances of this complex case, the combination of these factors denied the defendants’ due process right to a fair trial. First, it can be said that the defendants were denied reasonable notice and a fair opportunity to defend against the government’s allegations. The district court should have required the prosecution prior to trial to announce specifically the factual basis for its contention that the conspiracy continued into the limitations period. Thereafter the court should have adhered to that theory in its instructions and similarly limited the prosecution in its arguments to the jury. Lacking specific prior notice of the government’s factual scenario, the defendants were denied a fair opportunity to prepare and present evidence to rebut or defend against its contentions.
Second, this problem was compounded by the government’s apparent tactical decision to argue a new interpretation of the evidence in its rebuttal to the defendants’ closing arguments. The prosecutor — acknowledging that “I almost feel like I am going to ... reach behind my back and pull out a rabbit” — presented a reimbursement scenario different from and inconsistent with his previous argument, and thus denied the defendants an opportunity to respond and rebut his contentions.5
[803]*803Third, the government tainted the proceeding by suggesting in its closing arguments to the jury that the payments within the limitations period carried bribe money that was actually paid to Velazquez Toro, despite its prior concession in the jury’s absence that no evidence supported such an argument. It is impossible for us to determine whether the jury rested its finding of guilt on the impermissible ground suggested in the prosecutor’s closing, and therefore the judgments entered on the verdict must be set aside.6 Yates v. United States, 354 U.S. 298, 312, 77 S.Ct. 1064, 1073, 1 L.Ed.2d 1356 (1957); Government of the Virgin Islands v. Richards, 618 F.2d 242, 244 (3d Cir. 1980).
We therefore will reverse the judgments of conviction on counts 1, 4, and 7 and remand for a new trial; and we will require the government to inform the court and the defendants, at a reasonable date prior to retrial, of the specific theory on which it will attempt to prove that the conspiracy continued beyond September 4, 1975. If the prosecution elects on retrial to proceed on a theory of concealment to extend the conspiracy into the period of limitations, it should be required to meet the evidentiary burdens imposed by the Supreme Court in Grunewald v. United States, 353 U.S. 391, 77 S.Ct. 963, 1 L.Ed.2d 931 (1957). Specifically, it must present direct evidence that the conspirators originally expressly agreed to conceal the conspiracy, and it must show beyond a reasonable doubt that the September 5, 1975, transfer furthered that purpose. According to the teachings of Grünewald, neither circumstantial evidence permitting an inference of an agreement to conceal, nor direct evidence that the conspirators implicitly agreed to conceal, will satisfy the prosecution’s burden of production. Moreover, the government may not rely on evidence that the conspirators agreed to conceal their doings from GE’s internal auditors. Inasmuch as Vernon Twombly revealed the scheme to GE auditor Carl Mutch in June 1975, it is difficult to conclude that Twombly Inc.’s $94,441 payment to TEE in September 1975 could have furthered any such conspiratorial objective.
V.
Appellant Robert Naples argues that his resignation from GE effective August 29, 1975, constituted withdrawal from the conspiracy as a matter of law, and therefore that he cannot be prosecuted on an indictment returned more than five years after that date. The government has pointed to no evidence that Naples participated in the conspiracy in any way following his resignation, but it argues that his silence thereafter could be considered by the jury as evidence of his continuing participation. Because the government failed to produce evidence to rebut Naples' prima facie showing of withdrawal prior to the period of limitations, we hold that his convictions must be reversed on all counts.
The controlling precepts are familiar and require only a brief restatement. Mere cessation of activity in furtherance of an illegal conspiracy does not necessarily constitute withdrawal. The defendant must present evidence of some affirmative act of withdrawal on his part, typically either a full confession to the authorities or eommu[804]*804nication to his co-conspirators that he has abandoned the enterprise and its goals. See United States v. United States Gypsum Co., 438 U.S. 422, 464-65, 98 S.Ct. 2864, 2887, 57 L.Ed.2d 854 (1978); United States v. Lowell, 649 F.2d 950, 955 & n.7 (3d Cir. 1981). When a defendant has produced sufficient evidence to make a prima facie case of withdrawal, however, the government cannot rest on its proof that he participated at one time in the illegal scheme; it must rebut the prima facie showing either by impeaching the defendant’s proof or by going forward with evidence of some conduct in furtherance of the conspiracy subsequent to the act of withdrawal. See United States v. Lowell, 649 F.2d at 959-60 & n.16; United States v. Goldberg, 401 F.2d 644, 648-49 (2d Cir. 1968), cert. denied, 393 U.S. 1099, 89 S.Ct. 895, 21 L.Ed.2d 790 & 394 U.S. 932, 89 S.Ct. 1202, 22 L.Ed.2d 461 (1969).
Application of these precepts to this record requires reversal of Naples’ convictions. Naples presented evidence that he resigned and permanently severed his employment relationship with GE in August 1975. In the circumstances of this case, that was sufficient to make out a prima facie case of withdrawal and to shift the burden of production to the government. Had the government impeached or rebutted Naples’ evidence, the question properly would have gone to the jury. The government elected to stand on its proof, however, and therefore the district court erred in denying Naples’ motion for a judgment of acquittal pursuant to Fed.R.Crim.P. 29.
VI.
We now turn to appellants’ remaining contentions, most of which require little discussion. It is necessary for us to address their arguments that Puerto Rico is not a “State” within the meaning of the Travel Act, that the government abused the grand jury’s process, that the evidence was insufficient to sustain the convictions, that appellants Twombly, Inc. and GE withdrew from the conspiracy as a matter of law prior to the period of limitations, and that the Travel Act prosecutions are time-barred by application of the Puerto Rico statute of limitations for bribery prosecutions. We also consider appellants’ evidentiary arguments, although their resolution is not strictly necessary to decision of this appeal, to guide the parties and the trial court on remand. We find it unnecessary at this time to resolve appellant Steele’s objections to the instructions relating to his theory of defense.
The Travel Act, 18 U.S.C. § 1952, permits federal prosecutions based on the use of facilities of interstate commerce in furtherance of any “unlawful activity”; and it defines “unlawful activity,” insofar as it is relevant to this case, as “bribery ... in violation of the laws of the State in which committed.” The Travel Act prosecutions under indictment No. 80-73 and count 4 of No. 80-320 rest on the theory that the payments of May 28 and September 5,1975, furthered the unlawful activity of bribery in violation of the laws of Puerto Rico. Appellants argue that these counts must be dismissed because Puerto Rico is a Commonwealth within the federal union and not a “State” within the meaning of the act.
Our evaluation of this contention begins with the principles of statutory construction set forth in Puerto Rico v. Shell Co., 302 U.S. 253, 58 S.Ct. 167, 82 L.Ed. 235 (1937), in which the Court held that Puerto Rico was a “territory” within the meaning of § 3 of the Sherman Act. Whether Puerto Rico is a “state” within the meaning of § 1952
depends upon the character and aim of the act. Words generally have different shades of meaning, and are to be construed if reasonably possible to effectuate the intent of the lawmakers; and this meaning in particular instances is to be arrived at not only by a consideration of the words themselves, but by considering, as well, the context, the purposes of the law, and the circumstances under which the words were employed.
302 U.S. at 258, 58 S.Ct. at 169. Applying these principles, we have no difficulty re[805]*805jecting appellants’ argument. The limited legislative history demonstrates that Congress enacted the Travel Act at the insistance of Attorney General Robert F. Kennedy, who sought federal authority to assist “the States in combatting pernicious undertakings which cross State lines.” Letter of April 6, 1961, to the Speaker of the House, reprinted in H.R.Rep.No.966, 87th Cong. 1st Sess. 4, reprinted in 1961 U.S.Code Cong. & Ad.News 2664, 2666. The House Judiciary Committee explained that the act would “assist local law enforcement by denying interstate facilities to individuals engaged in illegal ... enterprises.” H.R.Rep.No.966 at 3, 1961 U.S.Code Cong. & Admin. News at 2665. The act “reflects a congressional judgment that certain activities of organized crime which were violative of state law had become a national problem. The legislative response was to be commensurate with the scope of the problem.” United States v. Nardello, 393 U.S. 286, 292, 89 S.Ct. 534, 537, 21 L.Ed.2d 487 (1969). We find no reason to hold that Congress (or the Attorney General, who submitted the draft legislation that became § 1952) chose the word “State” to deny Puerto Rican law enforcement the assistance extended to other localities within Congress’ power to protect, and such a construction would manifestly disregard “the character and aim of the act[,] .. . the context, the purposes of the law, and the circumstances under which the words were employed,” Puerto Rico v. Shell Co., 302 U.S. at 258, 58 S.Ct. at 169. We hold therefore that bribery in violation of Puerto Rican law is “bribery ... in violation of the laws of the State in which committed” within the meaning of § 1952.7
Appellants contend that the grand jury process was twice abused: first, that the one-count indictment against Twombly, Inc. was a “sham,” sought only to enable the government to gather information concerning additional charges and additional defendants, and therefore that both indictments should have been dismissed; and second, that the later indictment was based upon hearsay and therefore was improperly returned.
We reject both contentions. As to the first, the government — notwithstanding appellants’ present accusation that it concealed the true purpose of the first indictment — candidly stated that it was investigating additional charges and other defendants, and it does not appear to have concealed its knowledge that Bermuda courts would order the depositions of Bermuda residents only if there were an outstanding indictment. That the one-count indictment might assist the government to expand its investigation does not render it a sham, [806]*806because it is clear that the indictment was more than a mechanism to open the doors of the Bermuda courts. First, it does not appear, and appellants do not argue, that the first indictment was sought without probable cause. Second, the information the government was able to obtain because of the first indictment clearly related to that charge. To the extent that the information obtained served also as a foundation for the second indictment, that indictment concerned the same illegal scheme. Third, and most significant, the government actually pursued the prosecution and Twombly, Inc. was ultimately convicted under the first indictment. We conclude, therefore, that the district court did not abuse its discretion in denying appellants’ motions to dismiss the two indictments.8
Appellants also argue that they were deprived of their right to be tried only upon a properly returned indictment. They accuse the government of misleading the grand jury with hearsay evidence that inaccurately characterized the position of GE employee Frank Ayer. Ayer did not testify before the grand jury; rather, a Customs Service agent presented testimony based on notes Ayer had written during meetings of the scheme’s participants. Appellants contend that if Ayer had testified, he would have contradicted the implication of the agent’s hearsay testimony that the residual fuel equipment carried a portion of the bribe fund. The presentation of hearsay evidence, in appellants’ view, kept from the grand jury critical exculpatory evidence concerning the statute of limitations issue.
We have held that an indictment may be based upon hearsay evidence, United States v. Wander, 601 F.2d 1251, 1260 (3d Cir. 1979), and appellants’ arguments fail to persuade us that the government’s use of the hearsay evidence in this case requires invalidation of the indictments. The government did not misrepresent the hearsay testimony as a more reliable form of evidence. Moreover, although the grand jury did not hear it from Ayer himself, the defense’s theory on the statute of limitations issue was accurately summarized by the prosecutor. We therefore reject appellants’ contention that the indictment was improperly returned.
Appellant Schenectady Turbine Services challenges the sufficiency of the evidence to support its conviction. We think the evidence, while not overwhelming, was sufficient to allow the jury to find beyond a reasonable doubt that Schenectady was guilty as charged. The government presented evidence designed to show that Schenectady — through its agent and majority stockholder Mothon, who negotiated both sides of the Schenectady-TEE contracts — actively participated in the criminal enterprise, and we cannot fault the jury for crediting that evidence 'and drawing the inferences urged by the prosecution therefrom.
D.
Appellants GE and Twombly, Inc. argue separately but similarly that the evidence was insufficient to sustain their convictions because the government’s proof was inconsistent with certain language used in the two indictments. Indictment No. 80-73, which charges Twombly, Inc. in a single count with violating the Travel Act, alleges that Twombly, Inc., after May 28, 1975, “caused the deposit of an additional $377,765.98 to the account of Turbo Electric Equipment Ltd. at the Bermuda National Bank from which a bribe was to be paid to a Puerto Rican official.” Indictment No. 80-320 alleges that a purpose of the scheme was to “disguise and conceal the bribe fund to be paid to Carlos Velazquez Toro . .. . ” Focusing on the use of the future tense— “to be paid” — Twombly, Inc. contends that its conviction at No. 80-73 must be reversed because there is no evidence that Velazquez Toro received any of the “additional $377,-[807]*807765.98”; and GE argues that convictions obtained by proof of concealment of an accomplished bribe represent an unconstitutional amendment of the indictment. We reject these contentions; appellants make too much of the semantics and disregard the substance of the charges. The language of the indictments was ambiguous, but it did not deny the defendants reasonable notice. Twombly, Inc.’s argument rests on the assumption that Toro was to receive a bribe directly from the additional $377,-765; the government correctly responds that the indictment would permit proof, and that it did prove, that Toro was paid a bribe from the TEE account. GE’s argument fails because nothing was stated in the indictment suggesting that the purpose of concealment came to an end after Toro received the money; the language quoted simply speaks as of the time the agreement was formulated, when the bribe was “to be paid.”
E.
Twombly, Inc. contends that it withdrew from the conspiracy as a matter of law in June 1975, when Vernon Twombly revealed the scheme to GE auditor Carl Mutch; and GE argues that it withdrew as a matter of law before September 4, 1975, by commencing an investigation in response to Twombly’s disclosures. We disagree. Rather, we agree with the trial court that under the evidence of record the question of withdrawal prior to the period of limitations was properly left to the jury.
F.
Appellant Hoyt Steele argues that all Travel Act charges are time-barred because the applicable statute of limitations is not 18 U.S.C. § 3282 (five years) but the Puerto Rico statute that limits prosecution for the predicate offense, P.R.Laws Ann. tit. 33, § 4363 (three years). We disagree. “It must be made clear that 18 U.S.C. § 1952 charges a Federal crime,” United States v. D’Amato, 436 F.2d 52, 54 (3d Cir. 1970), and the relevant statute of limitations must be found in federal law. United States v. Cerone, 452 F.2d 274, 286-87 (7th Cir. 1971), cert. denied, 405 U.S. 964, 92 S.Ct. 1168, 31 L.Ed.2d 240 (1972). As we said in United States v. Forsythe, 560 F.2d 1127, 1134 (3d Cir. 1977), a case under the RICO statute, 18 U.S.C. §§ 1961 et seq., “[h]ad Congress intended state statutes of limitations to apply to a federal criminal statute it would have so stated.”
G.
Appellants launch a three-pronged attack on the admission of Bermuda bank records and videotaped depositions introduced to prove that Mothon actually paid the $1.25 million bribe to Velazquez Toro. They argue that the bank records were inadmissible hearsay; that use of the depositions violated Fed.R.Evid. 804(b)(1) and the Confrontation Clause, U.S.Const. amend. VI; and that both categories of evidence were irrelevant.
The government offered the bank records under Fed.R.Evid. 803(6), the hearsay exception for business records; but the district court — apparently on its own motion-admitted them pursuant to Rule 803(24), the “catch-all” exception.9 The government steadfastly maintains that the records are admissible under Rule 803(6), and it alternatively defends the district court’s [808]*808ruling under Rule .803(24). Appellants argue to the contrary, contending that the court erred in admitting the evidence under Rule 803(24) because the government did not give advance notice that it intended to rely on the rule. We need not reach these contentions given our decision that Counts 1, 4 and 7 must be re-tried and our conclusion that their admissibility, if erroneous, was harmless as to the conviction of Twombly, Inc. which is affirmed herein. We suggest, however, that if the issue arises at the new trial the court should ensure that the element of trustworthiness required under Rule 803(24) and the requirements of Rule 803(24)(C) are fully satisfied.
Appellants rely on Fed.R.Evid. 804(b)(1), which permits substantive use of deposition testimony only when the witness is unavailable and the party against whom his testimony is offered “had an opportunity and similar motive to develop the testimony by direct, cross, or redirect examination.” See also Fed.R.Crim.P. 15(e). Rule 804(a)(5) defines unavailability as absence from the trial when “the proponent of [the witness’ prior] statement has been unable to procure his attendance ... by process or other reasonable means.” The Confrontation Clause of the sixth amendment permits such evidence when “the witness is unavailable despite good-faith efforts undertaken prior to trial to locate and present that witness. As with other evidentiary proponents, the prosecution bears the burden of establishing this predicate.” Ohio v. Roberts, 448 U.S. 56, 74-75, 100 S.Ct. 2531, 2543, 65 L.Ed.2d 597 (1980). We have carefully reviewed the record and the submissions of the parties, and we hold that the district court neither erred nor abused its discretion in permitting introduction of the depositions.
We reject appellants’ contention that the evidence was irrelevant. “ ‘Relevant evidence’ means evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence,” Fed.R.Evid. 401. “The standard of relevance established by [Rule 401] is not high,” Carter v. Hewitt, 617 F.2d 961, 966 (3d Cir. 1980), and once the threshold of logical relevancy is satisfied the matter is largely within the discretion of the trial court, see Hamling v. United States, 418 U.S. 87, 124-25, 94 S.Ct. 2887, 2911, 41 L.Ed.2d 590 (1974). The disputed evidence, which indicated that Mothon had delivered approximately $1.25 million to Velazquez Toro in Bermuda in 1974, when considered together with other evidence in this case, manifestly made more probable the existence of a scheme to pay Velazquez Toro to manipulate the contract selection in favor of GE; and the district court did not err or abuse its discretion. Nor did the court abuse its discretion in determining that the relevance of the evidence outweighed its potential for causing unfair prejudice. Fed.R.Evid. 403.
We also reject the contention that Mothon should have been given limited immunity to testify that he and Velazquez Toro had entered into other transactions, thus vitiating the relevance of the government’s evidence. Defense witness immunity “will be denied if the proffered testimony is found to be ambiguous, [or] not clearly exculpatory . . . . ” Government of the Virgin Islands v. Smith, 615 F.2d 964, 972 (3d Cir. 1980). The defendants’ proffer did not indicate that Mothon would directly connect the payments in question to any other transaction. The requested immunity therefore was properly denied on the ground that the evidence would be ambiguous and not clearly exculpatory.
H.
Appellants argue also that the district court erred and abused its discretion in allowing the government to take testimony by deposition in Bermuda, because the depositions were taken for purposes of discovery and pursuant to a Request for International Judicial Assistance, or “letter rogatory,” which the district court had no au[809]*809thority to issue. These contentions require only a brief discussion.
We recognize that Fed.R. Crim.P. 15, which provides for the taking of depositions in criminal cases, does not authorize their use as means of discovery;10 but we cannot agree with appellants that the depositions at issue were used as discovery tools. Appellants emphasize that the government could not demonstrate to the district court the materiality of the proposed testimony. In view of the government’s inability to gain access to the proposed deponents, however, we agree with the district court that under the extremely unusual circumstances of this case it could not insist on the usual showing of materiality. In the ordinary case, where the witnesses reside in the United States, the witness who will be unavailable for trial will be available sometime prior to the deposition so that the parties will know with reasonable certainty the materiality of the proposed testimony. We believe that the district court appropriately accepted a reduced showing of materiality to avoid denying important evidence to all the parties, including the appellants, the court, and the jury.
Appellants’ argument that a district court in a criminal ease may not issue Requests for International Judicial Assistance, or letters rogatory, also fails. Fed.R. Crim.P. 15(d) directs that depositions are to be taken in the manner provided in civil actions, and Fed.R.Civ.P. 28(b)(3) authorizes the taking of depositions in foreign countries “pursuant to a letter rogatory.” Therefore, the district court did not err in issuing the disputed Request.
Appellants contend that the court erred in permitting GE employee Frank Ayer to read certain notes to the jury over a hearsay objection, pursuant to Fed.R. Evid. 803(5).11 We do not agree. The court heard Ayer testify extensively on voir dire, and it carefully limited admission to those portions of the notes that satisfied the requirements of Rule 803(5). Appellants’ objection that Ayer lacked personal knowledge of the matters recorded is irrelevant. The notes were introduced to prove the declarations of co-conspirators, which are non-hearsay under Fed.R.Evid. 801(d)(2)(E), and not to prove directly the truth of the matters stated. Nor did the court err or abuse its discretion in permitting Ayer to interpret the notes to the jury; once the notes were admitted under Rule 803(5) they were subject to testimonial interpretation the same as any ambiguous document properly admitted in evidence. We also reject the suggestion that the court abused its discretion in determining that the notes’ probative value outweighed their potential for unfair prejudice, Fed.R.Evid. 403.
J.
We are more sympathetic to appellant Steele’s objections to the court’s instructions to the jury. Steele first submitted proposed instructions outlining his contentions and their significance for his theory of defense, and his counsel thereafter agreed with the prosecutors to submit a modified set of instructions designed to avoid the government’s objections to his initial proposal. Notwithstanding the government’s acquiescence in the revised [810]*810proposal, however, the court declined Steele’s request and relied on a standard formbook of jury instructions. Standard form instructions should “not be swallowed whole”; they are designed “as an aid to the preparation of an appropriate instruction in the particular case.... Each case has its own peculiar facts and formalized instructions must be tailored to the requirements of. the facts and issues.” 1 E. Devitt & C. Blackmar, Federal Jury Practice and Instructions § 8.03 at 247 (3d ed. 1977). We need not decide whether the court committed a reversible abuse of discretion in rejecting Steele’s proposed instructions, because there must be a new trial in any event. A district court should be extremely cautious in rejecting a defendant’s proposed instructions in the absence of a specific objection from the government, however, and it should indicate on the record the reasons for its decision to do so.
VII.
The judgment of the district court on indictment No. 80-73 will be affirmed. The judgments of conviction and sentence on counts 2, 3, and 5 of indictment No. 80-320, and appellant Robert Naples’ convictions on all counts, will be reversed on the basis that directed verdicts of acquittal should have been entered. The remaining judgments of conviction and sentence on counts 1, 4, and 7 of indictment No. 80-320 will be reversed and the cause remanded for a new trial on these counts in accordance with the foregoing.