WINTER, Circuit Judge:
Appellants are a group of union and construction company officials who have been convicted by a jury before Chief Judge Platt of a panoply of labor racketeering charges, including conspiracy, extortion, labor bribery, RICO conspiracy, and associated crimes such as obstruction of justice, perjury, and the making of false statements. The various appellants, the precise charges on which they were convicted, and their resultant sentences are noted in the margin.1 Except for a reversal of certain labor bribery convictions, we affirm.
[336]*336BACKGROUND
Appellants were charged along with twelve others in a 102-count indictment. The allegations centered on corruption in the affairs of Mason Tenders’ Local Union 13 of the Laborers International Union of North America (“Local 13”) and the Mason Tenders’ District Council of Greater New York Trust Funds (“Trust Funds”). Local 13 and the Trust Funds, in their relationship with construction industry corruption, were alleged to constitute a racketeering enterprise under the Racketeer Influenced and Corrupt Organizations Act (“RICO”), 18 U.S.C. § 1961(4) (1988). Codefendant Basil Robert Cervone, whose appeal was withdrawn, was business manager of Local 13 and an officer and Union Trustee of the Trust Funds. Appellants Peter Vario and Henry Walaski were also labor union officials. Vario was business manager of Mason Tenders’ Local Union 46 (“Local 46”), and Walaski was business agent of Local 531 of the Brotherhood of Carpenters and Joiners of North America (“Local 531” or “Carpenters”), whose territory overlapped with Local 13’s.
The other appellants were all construction company officials. Edward Cummings was a site supervisor for Benjamin Contracting Corp., a developer and builder of residential properties in the New York area. Albert DiBernardo was president of Cadin Contracting Corp., a firm used by Benjamin Contracting as a subcontractor. Anthony Perna was owner-operator of Per-na Contracting Co., a general contractor from Whitestone, New York. George Ber-nesser was owner and president of Bernes-ser Masonry Corp. Cummings, DiBernar-do and Perna were convicted of participating in labor bribery with Cervone, while Bernesser was convicted of impeding the investigation of corruption in Local 13.
The evidence showed a network of corruption in the construction industry, involving construction company and union officials who engaged in a pattern of labor bribery and extortion. We recite only those facts pertinent to the appealed counts of conviction.
1. Vario and Walaski
Appellants Vario and Walaski came into contact with Cervone’s Local 13 in their capacity as business agents for Local 46 and for the Carpenters local respectively. Pertinent to their convictions on various charges, see supra note 1, was evidence regarding dealings between Cervone and Vario and the Viti Construction Corp. (“Viti Corp.”), a concrete contracting firm. Cer-vone had threatened to unionize Viti Corp.’s workforce in the late 1970’s, but had relented as a result of an agreement with Julio Viti, the firm’s owner, that Viti Corp. would make a cash payment of $50— later increased — personally to Cervone for every house foundation poured by Viti Corp. Cervone also demanded Christmas “gifts” of liquor and cash. A taped telephone conversation implicated Walaski in [337]*337Viti Corp.’s 1984 holiday gift to Cervone. In that conversation, Julio Viti told Cer-vone that before they could meet that day he (Viti) had to “go see Hank around eleven.” In reply, Cervone instructed Viti to give Cervone’s “gift” to Walaski: “Give it to Hank [Walaski], whatever you gotta do, ya understand, and tell Hank, say listen, bring this to Bobby.” Later that day Viti delivered Cervone’s present to Walaski, along with an additional gift of liquor and cash for Walaski to keep for himself. This gift was the basis for Walaski’s conviction on Count 34 for labor bribery.
Vario’s and Walaski’s convictions also involved the enterprise’s dealings with three Queens construction companies: Q.V. General Mason Co., Inc., Q.V. Scaccia General Mason, Inc. (the “QV Companies”), and Sa-nita Construction Corp. (“Sanita Corp.”). These firms were run by Christopher Scac-cia and his son-in-law, Americo Sanita. Cervone, Walaski and Vario, acting in concert, extracted payoffs for labor peace from the QV Companies and Sanita Corp. in the mid-1980’s.
Part of Walaski’s role in the extortion was to assign a troublemaking Carpenters shop steward to a QV job site in Queens. Scaccia, having attempted without success to have Walaski remove the steward, contacted Cervone, who assured him that the problem steward would be replaced. In an intercepted phone conversation on March 27, 1985, Cervone and Walaski discussed the situation:
Walaski: Hey, Mr. Soaccia’s down on his knees. He’s beggin ...
Cervone: (Laughter)
Walaski: He’s beggin me to give him a foreman.
Cervone: (Laughter) I ... I ... I ... I ... I told him that the ah ... his best bet is to get a couple of men from you and ah listen to you. I told him in the car for 15 minutes.
Walaski: Yea.
Cervone: Maybe he got convinced.
Walaski: Yea.
Cervone: Did you take that guy away from him?
Walaski: Wh ... which guy?
Cervone: The one that he ... that he don’t want?
Walaski: No, he’s stayin’ there.
Cervone: Oh yea (laughter).
Later that day, after Cervone and Wala-ski had again discussed the matter, Scaccia had the following conversation with Cer-vone:
Cervone: Oh well (In Italian) (Leo, I spoke to that guy I made an agreement.)
Scaccia: Oh, umm.
Cervone: You know I already wanted (In Italian) (to keep my word).
Scaccia: Yeah but, (In Italian) (in cash?)
Cervone: Huh?
Scaccia: You want it (in Italian) (only in cash?)
Cervone: Yeah sure, might as well ‘cause, get it over with. You know (In Italian) (keep your word, this way, this way when t hat [sic] guy tells me a thing.)
Scaccia: [unintelligible] no.
Cervone: Huh?
Scaccia: (Three?) no?
Cervone: Yeah, all right uh, (In Italian) (tomorrow) you could do that (In Italian) (tomorrow). (This way I make one time at the office.) This way good bye — good luck ’cause he, took the man away from you.
A notebook belonging to Scaccia indicated two payments of $3000 to Walaski, one on April 4, 1985 and the other on April 26. The book also showed payments of $2500 and $3000 to Cervone in the same period. This evidence was the basis for Walaski’s conviction on Count 45 of aiding and abetting Cervone’s Hobbs Act extortion. Scaccia and Sanita also executed a series of “ghost” checks to fictitious employees and turned them over to Cervone in return for his influence in the matter of the Carpenters shop steward. These checks were the support for Walaski’s convictions on Counts 46-51 for aiding and abetting Cervone’s labor bribery.
Vario assisted Cervone in a separate transaction with Sanita Corp. In November 1985, after learning that the QV Com-[338]*338pañíes and Sanita Corp. had undertaken a job in Corona, Queens, without notifying him, Cervone informed Americo Sanita that Yario would be visiting another Sanita Corp. jobsite in Far Rockaway to collect “the dues.” In intercepted phone conversations on November 13 and 14, Cervone instructed Vario to “let him [Sanita] come running,” and to “[tjhrow the agreement at him and everything.” He also stated that Vario should “tell him that you spoke to me” in order to “show him that we’re working together,” and that Vario should “find out what the dues are going to be and ask [Sanita] for the dues.” In response to Cervone’s telling him that Vario would be visiting the Far Rockaway jobsite to collect dues, Sanita gave Cervone a check for $1300. These facts were the basis for Vario’s conviction on Count 53 for aiding and abetting Cervone’s receipt of a labor bribe.
Vario and Walaski were also involved, along with Cervone and another codefend-ant, Joseph Frangipane, in a series of payoffs for labor peace from the Spartan Concrete Corp. (“Spartan”). Frangipane was the business agent of the Cement and Concrete Workers Local Union 20 (“Local 20” or “Concrete Workers”), whose territory included a Spartan jobsite on Atlantic Avenue in Queens. The site was also arguably within the jurisdiction of Vario’s Mason Tenders’ Local 46, which handled certain jobs involving concrete. Although Martin Padover, Spartan’s president, had reported the job to the District Council of Cement and Concrete Workers Unions as required under the collective bargaining agreement, Vario, upon learning of the project, took the position that it was a Mason Tenders’ job, rather than one for the Concrete Workers.
Padover sought Cervone’s intervention to establish which union had jurisdiction. Cervone and Vario agreed that the job likely fell under the authority of both unions, and Cervone therefore arranged that Pad-over would pay bribes to officials of both. Frangipane was paid off through “ghost” paychecks, while Vario, despite Padover’s view that Atlantic Avenue was a Concrete Workers’ job, received a cash payment of $1000, “just to start off the relationship.” This payment was the basis of Vario’s conviction on Count 61 for labor bribery.
Walaski received a bribe from Padover that involved the Pak Realty construction project, a Spartan job on Northern Boulevard in Queens. Although Padover had previously paid off Cervone for labor peace on this and another job, Walaski, through the same troublesome shop steward he had used to coerce the QV Companies, began to cause difficulties at the Pak Realty site. In order to get the steward to stop “bust[ing] chops,” Padover sought Cer-vone’s help in placating Walaski. At a March 29, 1985 meeting in the parking lot of Leonard’s of Great Neck, attended by Padover, Cervone, and Walaski, Padover turned over $5000 cash and two checks to Cervone and gave Walaski an envelope containing $800 cash. These transfers were the basis for Walaski’s convictions on Count 66 for labor bribery, regarding his own receipt of $800, and on Count 65 for aiding and abetting Cervone’s simultaneous receipt.
Finally, in April 1983, Vario accepted a $2350 payment from Padover regarding two Spartan concrete jobs on a project called Airgate, within Local 46’s territory. As agreed in April, Padover supplemented this with another $2000 payment to Vario in September, bringing the total bribe on the Airgate jobs to $4350, one percent of Spartan’s contract price on the construction. These payments were the basis for Vario’s conviction on Count 67 of labor bribery.
2. Perna
Anthony Perna was owner-operator of Perna Contracting Corp., a general contractor operating in Manhattan and Queens. In October 1985, Perna telephoned Cer-vone, with whom he had been acquainted for some years, to tell him that he wished to see him the next week. Six days later, Perna again called Cervone to tell him he had “something to give” to him. He indicated that Cervone or a surrogate should come to Perna Contracting’s offices after 3:00 p.m. the following day. He also ex[339]*339plained that, in the event Cervone himself would not be coming by, the item to be picked up would be placed in a “busta” (Italian for envelope) for him. Immediately after speaking with Perna, Cervone called John Cerasuolo, a Local 13 shop steward, and instructed him to go to Perna’s office the following afternoon at 3:30. Cerasuolo briefly visited Perna’s office the next day and then returned to Local 13 headquarters. Shortly thereafter, Cervone received a call from an unidentified female who said, “Okay, this is Perna CONTRACTING. You sent John here and we gave him an envelope.” Cervone answered affirmatively. She asked further whether he, Cer-vone, had received it. Again he answered “Yes,” and he gave the same answer to Perna when he came on the line and inquired after the envelope.
On December 16 and 17, 1985, Perna and Cervone communicated about another “little package,” with Cerasuolo again acting as courier. Cerasuolo and Perna called Cervone from Perna’s office, and the three discussed an envelope from Perna for Frank Alessi of Bricklayers Local 41. After inquiring whether Alessi had “treat[ed] [Perna] all right,” Cervone told Perna to give the envelope to Cerasuolo to carry to Cervone, who would give it to Alessi. These transactions were the basis for Per-na’s conviction on Count 88 of labor bribery.
On July 22, 1986, Perna was interviewed at his office by law enforcement personnel, including a federal agent. In response to the agent’s inquiries, he asserted that he had “never” made payoffs to Cervone or anyone else for labor peace. He denied that Cervone had ever tried to solicit a bribe. He also denied ever having given an envelope to Cerasuolo and asserted that no one from Local 13 had ever visited his office for such a purpose. These answers were the basis for his conviction on Count 98 for false statements.
3. Cummings and DiBernardo
In 1985, Albert DiBernardo was the president of Cadin Contracting Corp. (“Cadin”), and Edward Cummings was a site supervisor for Benjamin Contracting Corp. (“Benjamin”), the firm for which Cadin was then engaged as a masonry subcontractor on the Cunningham Park Condominium Project in Queens. In July 1985, certain groups claiming to represent minority construction workers began demonstrating at the Cunningham Park jobsite, demanding that Cad-in hire from their ranks. Cummings contacted Cervone to seek his intervention. On July 10, Cervone told DiBernardo in an intercepted conversation that it would be necessary to “bring some cash” in order to solve the problem. On July 26, Cervone met with Earl Ferguson, head of the Queens Minority Association, one of the protesting coalitions, and gave him $1000 cash. In arranging that meeting, Cervone had told Ferguson over the phone that he was awaiting $1000 in “dues” from someone, asked if Ferguson was “following” him on that, and explained that he would call again when the “dues” had been received. After setting up the meeting with Ferguson, Cervone told Cummings that he had “kept the blacks away” from him.
He was wrong, however. Bob Patterson, a rival minority coalition leader, continued to pressure Cadin to hire coalition workers for the Cunningham Park project. Cummings telephoned Cervone on July 30 to report that Patterson was threatening “stopping the job.” DiBernardo was observed a week later passing an envelope to Cervone at the Leonard’s of Great Neck parking lot. The evidence regarding the Cunningham Park events was the basis for Cummings’ and DiBernardo’s convictions on Count 83 for conspiracy to commit labor bribery and DiBernardo’s conviction on Count 85 for the substantive offense. Cummings was also convicted on Count 97 for a false statement on the basis of his denial, in a July 16, 1986 interview at his office with New York City police detectives, of ever having spoken to Cervone about the coalitions or about minority hiring practices.
4. Bernesser
George Bernesser, president of Bernes-ser Masonry Corp. (“Bernesser Masonry”), [340]*340contacted Cervone in late 1985 regarding a masonry subcontract for work at Shea Stadium that was to be awarded through competitive bidding. In order to preclude the introduction of potentially uncooperative out-of-town contractors, Cervone decided to assist Bernesser Masonry in obtaining the job and informed Bernesser of the price quoted in one of the sealed bids submitted by a competitor so that he might fashion his own bid accordingly. Ultimately, the contract was awarded to another firm for a lower figure, causing Bernesser to phone Cervone and complain that the winner in actuality had submitted a “[ljower number than you told me.”
On July 10, 1986, Bernesser was interviewed by F.B.I. agents regarding corruption in the construction industry. He stated that he knew Cervone, but denied any involvement in bid rigging. Four days later, he appeared before a federal grand jury and gave the following testimony:
Q. It is your practice to discuss the bids you are submitting on pending projects to Mr. Cevone [sic]?
A. No.
Q. Have you ever done that?
A. No.
Q. Has Mr. Cevone [sic] ever given you the number being bid by another contractor?
A. No.
Q. It’s never happened?
A. Not to me.
Q. Who got the job at Shea Stadium, project number two, that you didn’t get?
A. I don’t know.
Q. Did you ever go back to find out? Did you ever find out what the number was?
A. No.
These episodes were the basis of Bernes-ser’s convictions on Count 26 for obstruction of justice and on Count 96 for perjury.
At trial, Bernesser’s theory was essentially that he was not actively engaged in running the masonry business at the time of the Shea Stadium bidding, and that he was then taking medication for a benign tumor. Bernesser claimed that one of the side effects of this medication was short-term memory loss, and that his inaccurate statements were without criminal intent. In support of the medical aspect of this theory, counsel sought to call witnesses to testify to Bernesser’s having taken certain drugs and to the side effects of those drugs. The court, however, refused to admit the testimony, holding that a letter advising the government of the possibility of such testimony was untimely under Fed. R.Crim.P. 12.2(b).
DISCUSSION
As many of the grounds urged for reversal are pressed by more than one appellant or are otherwise related, the organization of our analysis will be governed by the nature of the claim.
1. Joinder/Sever anee
Four of the appellants — Perna, Vario, Di-Bernardo, and Walaski — make some manner of claim regarding their having been tried together in a single proceeding. Di-Bernardo and Perna argue that their join-der in this indictment was improper under Fed.R.Crim.P. 8(b).2 They further argue, as do Vario and Walaski, that Chief Judge Platt’s refusal to grant them severances was an abuse of discretion in light of prejudicial “spillover” evidence.
Rule 8(b) of the Federal Rules of Criminal Procedure governs questions of join-der.3 The rule states that participation of [341]*341multiple defendants in the “same act or transaction,” or the same “series” of such acts, will authorize joint trial on common or individual counts. We have construed this language to mean that joinder is proper where two or more persons’ criminal acts are “ ‘unified by some substantial identity of facts or participants,’ or ‘arise out of a common plan or scheme.’ ” United States v. Attanasio, 870 F.2d 809, 815 (2d Cir.1989) (quoting United States v. Porter, 821 F.2d 968, 972 (4th Cir.1987), cert. denied, 485 U.S. 934, 108 S.Ct. 1108, 99 L.Ed.2d 269 (1988)). Joinder of defendants is reviewed as a question of law. United States v. Lane, 474 U.S. 438, 449 n. 12, 106 S.Ct. 725, 732 n. 12, 88 L.Ed.2d 814 (1986); United States v. Turoff, 853 F.2d 1037, 1042 (2d Cir.1988).
Because we reverse DiBernardo’s convictions on other grounds, we need address only Perna’s claim of improper joinder. The link between Perna and the rest of the indicted defendants is somewhat tenuous. He was the only defendant charged in the two counts naming him. He was not charged in the RICO conspiracy count or in any of the underlying racketeering acts, and he was the only one of the eighteen defendants not charged jointly in any count in the indictment with a defendant named in the RICO count. Chief Judge Platt denied the severance motion as to Perna on the ground that the indictment tied Perna to Cervone because Count 88 identified Cervone as the recipient of the labor bribe charged against Perna. United States v. Cervone, No. 87-CR-579, slip op. at 34, 1988 WL 155641 (E.D.N.Y. May 12, 1988) (Memorandum and Order).
The government argues that Count 87, a labor bribery charge against Cervone that was also a RICO racketeering act, was so “integrally related” to Count 88, in which Perna was charged with making the same payment at issue in Count 87, that joinder was proper under Rule 8(b). At oral argument the government maintained that Counts 87 and 88 could easily have been combined into a single count. This peculiarity in the drafting of the indictment is difficult to explain, but the counts do concern common defendants and a common scheme involving a single labor bribe, so that joinder of Perna, though perhaps of limited benefit in the way of judicial economy, did not run afoul of Rule 8(b).
The severance motions incorporated a request for severance under Fed.R. Crim.P. 14,- which allows the court in its discretion to sever charges or defendants, even where they have been properly joined, if failure to do so would prejudice the defendant. A motion under the rule is committed to the sound discretion of the trial court and is “virtually unreviewable.” United States v. Friedman, 854 F.2d 535, 563 (2d. Cir.1988) (quoting United States v. Stirling, 571 F.2d 708, 733 (2d Cir.) (quoting 8 J. Moore, Moore’s Federal Practice 1114.02[1], at 14-3 (2d ed. 1977)), cert. denied, 439 U.S. 824, 99 S.Ct. 93, 58 L.Ed.2d 116 (1978)), cert. denied, — U.S. -, 109 S.Ct. 1637, 104 L.Ed.2d 153 (1989). It is thus not sufficient to show a likelihood that a separate trial would have benefitted the defendant. Rather, there must have been prejudice so substantial as to amount to a “miscarriage of justice.” United States v. Nersesian, 824 F.2d 1294, 1303 (2d Cir.) (quoting United States v. Bari, 750 F.2d 1169, 1177 (2d Cir.1984), cert. denied, 472 U.S. 1019, 105 S.Ct. 3482, 87 L.Ed.2d 617 (1985)), cert. denied, 484 U.S. 957, 108 S.Ct. 355, 98 L.Ed.2d 380 (1987); see United States v. Chang An-Lo, 851 F.2d 547, 556 (2d Cir.), cert. denied, 488 U.S. 966, 109 S.Ct. 493, 102 L.Ed.2d 530 (1988).
Appellants have not met this burden. First, the court twice delivered a limiting instruction designed to safeguard against the possibility of “spillover” prejudice, telling the jury to:
analyze what the evidence in the case shows with respect to [each defendant], leaving out of consideration entirely any [342]*342evidence admitted solely against some other defendant or defendants. Each defendant is entitled to have his case determined from evidence as to his own acts, statements and conduct, and any other evidence in the case which may be applicable to him.
Except for isolated instances of confusion between the court and counsel regarding the admissibility of certain evidence as to certain defendants, there is no indication of prejudice. Vario, Walaski, and Perna were each accused of analytically discrete instances of corrupt interaction with Cervone and Local 13, each of which easily could have been considered separately by the jury. Even as to Perna, for example, the charges against him were based largely on recorded phone calls in which he participated. This was not a case, therefore, in which spillover might influence a jury to attribute criminal intent to ambiguous conduct associating a particular defendant with a conspiracy. In sum, appellants have failed to show that they suffered substantial prejudice from being tried with each other. See United States v. Casamento, 887 F.2d 1141, 1153 (2d Cir.1989), cert. denied, — U.S. -, 110 S.Ct. 1138, 107 L.Ed.2d 1043 (1990).
2. The Section 1001 Counts
Perna and Cummings argue that their convictions under 18 U.S.C. § 1001 for false statements to agents investigating a matter for an agency within the jurisdiction of the United States must be overturned under the so-called “exculpatory no” doctrine, which has been adopted by some federal courts. That doctrine immunizes direct denials of criminal wrongdoing made in response to questions, irrespective of their falsity, from prosecution under Section 1001. See, e.g., United States v. Cogdell, 844 F.2d 179, 182-83 & n. 3 (4th Cir.1988); United States v. Medina de Perez, 799 F.2d 540 (9th Cir.1986); United States v. Chevoor, 526 F.2d 178, 182-84 (1st Cir.1975), cert. denied, 425 U.S. 935, 96 S.Ct. 1665, 48 L.Ed.2d 176 (1976); United States v. Bush, 503 F.2d 813 (5th Cir.1974). Cummings submitted a request to charge based on the “exculpatory no” defense, but the court rejected it.4 This was not erroneous.
Cummings argues that we adopted the “exculpatory no” doctrine in United States v. Grotke, 702 F.2d 49, 52-54 (2d Cir.1983). The passage from Grotke that he quotes, however, is itself a quotation from United States v. Fitzgibbon, 619 F.2d 874 (10th Cir.1980), and was included in the Grotke opinion solely for purposes of describing the doctrine. Id. at 52. We have never adopted the doctrine, see United States v. Capo, 791 F.2d 1054, 1069 (2d Cir.1986), rev’d in part on other grounds on rehearing in banc, 817 F.2d 947 (2d Cir.1987), but have indicated that were we to adopt it, it would be construed narrowly, see id.
[343]*343Moreover, neither Perna nor Cummings would benefit from even a broad version of that doctrine. Perna was convicted under Section 1001 for his denials that Cerasuolo or anyone else affiliated with Local 13 had ever visited his offices to pick anything up. There would have been nothing directly inculpatory in a truthful answer to questioning regarding the simple fact of Cerasuolo’s visit, and even courts that have adopted the “exculpatory no” defense do not apply it to a non-exculpatory response. See United States v. Rose, 570 F.2d 1358, 1364 (9th Cir.1978) (“exculpatory no” doctrine not applied where truthful answer would not involve self-incrimination); cf. Cogdell, 844 F.2d at 183, 185; Medina de Perez, 799 F.2d at 546. Perna also denied making payoffs for labor peace. Perna’s denial of payoffs, however, was made in the context of a wide-ranging and discursive interview with agents who had identified themselves. He was not taken by surprise or otherwise cornered into a defensive, ill-considered misstatement. See United States v. McCue, 301 F.2d 452, 455 (2d Cir.) (because interviewee was “well aware of the nature and purpose of the examination,” the question of “the citizen who replies to the policeman with an ‘exculpatory “no” ’ can be left until it arises”), cert. denied, 370 U.S. 939, 82 S.Ct. 1586, 8 L.Ed.2d 808 (1962).
As to Cummings, his remarks were not truly exculpatory. Certainly no incriminating consequences were to be feared from a truthful answer to the inquiry as to whether he had even discussed minority hiring problems with Cervone. Even if the conversation with the officers had ended after that particular false statement, Cummings would have affirmatively misled them, perhaps causing them to direct their investigation elsewhere. Cummings’ denial of any talks regarding the minority hiring situation thus falls within the currently recognized ambit of the statute. See United States v. Rodgers, 466 U.S. 475, 479, 104 S.Ct. 1942, 1946, 80 L.Ed.2d 492 (1984).
3. Sufficiency of the Evidence
Perna, Bernesser, Vario, and Walaski raise meritless challenges to the sufficiency of the evidence underlying certain of their convictions. A defendant making such a challenge “bears a ‘very heavy burden.’ ” United States v. Buck, 804 F.2d 239, 242 (2d Cir.1986) (quoting United States v. Davis, 767 F.2d 1025, 1040 (2d Cir.1985) (quoting United States v. Soto, 716 F.2d 989, 991 (2d Cir.1983))). The jury’s verdict must be accepted if there is “substantial evidence” to support it. Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942). In reviewing an insufficiency claim, an appellate court must credit every inference that could have been drawn in the government’s favor. See id.; United States v. Bagaric, 706 F.2d 42, 64 (2d Cir.), cert. denied, 464 U.S. 840, 104 S.Ct. 134, 78 L.Ed.2d 128 (1983); United States v. Carson, 702 F.2d 351, 361 (2d Cir.), cert. denied, 462 U.S. 1108, 103 S.Ct. 2456, 2457, 77 L.Ed.2d 1335 (1983). We must affirm if, from the inferences reasonably drawn, the jury might fairly have concluded guilt beyond a reasonable doubt. Buck, 804 F.2d at 242; United States v. Taylor, 464 F.2d 240, 244-45 (2d Cir.1972). To be sufficient, moreover, the evidence need not exclude every “reasonable hypothesis which is consistent with innocence.” United States v. Fiore, 821 F.2d 127, 128 (2d Cir.1987).
Perna argues that his conviction on Count 88 for labor bribery was defective because the government failed to prove that he paid or delivered a “thing of value” to a union representative, an element of the offense. See 29 U.S.C. § 186(a) (1988). He observes that in all of the intercepted telephone conversations regarding Cerasuolo’s trips of October 18 and December 17, 1985 to his office to pick up envelopes, no one ever identified the contents of those envelopes. He concludes from this that the jury as a matter of law could not have concluded beyond a reasonable doubt that something of value was being transferred.
His description of the evidence is accurate, but his legal conclusion is faulty. The finding that bribes were involved easily could have been made on the basis of solid inferences from the evidence. The context [344]*344of the calls, the promptness with which Perna sought confirmation of the receipt of one of the envelopes, the studied non-identification of the items over the phone except as “bustas” or “little packages,” the importance attributed to them reflected in the calls, and the inquiry as to whether the Bricklayers union official had “treated [Perna] all right,” strongly suggest that the envelopes contained payoffs. Perna was of course free to argue to the jury that the envelopes were an innocent mystery, but the jury was also free to disbelieve him.
Bernesser challenges his perjury conviction on sufficiency grounds. He argues that his answers to the grand jury questions were literally true, if misleading, and that he was confused in the grand jury room. The confusion is said to have resulted from some ambiguity regarding which “phase” of the Shea Stadium project he was being questioned about and “rampant confusion in the questioning.” This attack also fails.
A perjury defendant may, at trial, portray the subject statements as literally true or unintentionally inaccurate, but it is ultimately for the jury to resolve, see Friedman, 854 F.2d at 560. Bernesser was asked whether “Cervone [had] ever given [him] the number being bid by another contractor.” His answer was, “No.” This question-and-answer was not clouded by any uncertainty attributable to the arcana of the Shea Stadium plans. Given Bernes-ser’s telephoned complaint to Cervone that Capri had been awarded the job for a figure “[l]ower than the number you told me,” the jury can hardly be faulted for finding his grand jury testimony literally and intentionally untrue. Moreover, we do not find those portions of the grand jury transcript cited as evidence of Bernesser’s general “confusion” to support that claim. Bernes-ser did evince some hedging and uncertainty about historical details—understandable in light of his accompanying distortions and untruths—but showed no difficulty grasping the questions put to him.
Vario and Walaski share an argument regarding the proof against them on Count 95, the RICO conspiracy. They contend that, because they were not formally affiliated with Local 13, the charged enterprise, the government was obliged to provide some tangible evidence of an agreement to become associated. The law, however, does not require one to carry a membership card or to appear on a signed membership roll. In order to convict under 18 U.S.C. § 1962(d), the jury had to find only that Vario and Walaski agreed to commit the substantive RICO offense by agreeing to participate in the racketeering acts related to the conspiracy, and that each knew the “general nature of the [RICO] conspiracy and that the conspiracy extend[ed] beyond his individual role.” United States v. Rastelli, 870 F.2d 822, 828 (2d Cir.), cert. denied, — U.S. -, 110 S.Ct. 515, 107 L.Ed.2d 516 (1989); United States v. Persico, 832 F.2d 705, 713 (2d Cir.1987), cert. denied, 486 U.S. 1022, 108 S.Ct.1995, 100 L.Ed.2d 227 (1988). There was a legion of evidence to support a finding of those elements.
Vario’s attack on his substantive conviction on Count 53 for labor bribery also fails. The jury was permitted to conclude that Vario agreed to act together with Cervone to extract the $1300 payment from Sanita. Vario’s principal complaint is that there was evidence to suggest that Sanita made the payment before Cervone and Vario agreed to seek the bribe. However, the evidence was also quite clear that Sanita remembered writing the check after a visit from Cervone, and a recorded call between Cervone and Vario, in which Cer-vone stated that he had threatened Sanita by invoking Vario’s name, might easily have been found by the jury to pertain to that visit.
Walaski’s insufficiency claims regarding his substantive convictions are similarly without merit. It is clear that the jury believed the “ghost” checks charged in Counts 46-51 were a reward for Cer-vone’s intervention in removing the ubiquitous, troublemaking shop steward, a person under Walaski’s authority. There was ample circumstantial evidence supporting that inference. Similarly, Walaski’s convic[345]*345tion on Count 65 for aiding and abetting Cervone’s receipt of a bribe from Padover is supported by the evidence. Walaski went along to the meeting and received his own bribe, but clearly was the instrument, through his deployment of the troublemak-ing steward, of Cervone’s own receipt of a separate bribe as a go-between or peacemaker. Finally, the jury’s conviction of Walaski on Count 45 regarding the Scaccia payoff cannot be seriously challenged. Once again the telephone tapes indicate that Walaski’s steward was the reason for the bribe. The indication in Scaccia’s notebook that Walaski was also paid off does not undercut the inference that Walaski was assisting Cervone but rather supports the conclusion that Walaski played an active and intentional role.
4. Amendment to the Indictment
Bernesser contends that he was convicted upon an improper amendment to the indictment because the perjury count in the indictment referred to the “second phase” of the Shea Stadium job and the evidence at trial regarding the rigged bidding concerned “Phase Three” of the project.5 See Stirone v. United States, 361 U.S. 212, 217, 80 S.Ct. 270, 273, 4 L.Ed.2d 252 (1960) (where “new basis for conviction” added by theory not presented in indictment, cannot assume jury convicted on original indictment theory); see also United States v. Zingaro, 858 F.2d 94, 98 (2d Cir.1988) (constructive amendment of indictment is per se violation of grand jury clause of Fifth Amendment).
The point is frivolous. The grand jury minutes make clear that it was Bernesser himself who introduced the idea of two distinct phases to the project at Shea. The indictment thus adopted the terminology used by him in the grand jury hearing. In any event, Bernesser categorically denied ever receiving competitors’ bid information from Cervone, and it is far from clear that a relabeling of the stages in the indictment would have made any difference. Moreover, the only testimony to contradict the indictment’s designation “second phase”— borrowed from Bernesser himself — would seem to have come from Bernesser’s son, George Jr., who introduced the three-phase structure in his direct testimony for the defendant.
5. Bernesser’s Medical Evidence
Bernesser asserts error in the district court’s refusal to admit medical testimony regarding the medications he was taking for his tumor and their side effects with respect to short-term memory. The court grounded its ruling on Bernesser’s failure to supply timely notice to the government and the clerk of the court of his intention to introduce such expert testimony, as required under Fed.R.Crim.P. 12.-2(b).6 Bernesser argues first that Rule 12.2(b) did not require notice for the kind of evidence he sought to introduce, and second, that even if it did, the letter to the government was adequate notice.
Bernesser describes the effects of the drugs upon his memory as a physical, rather than a mental, condition, and he therefore asserts that Rule 12.2(b) does not ap[346]*346ply. He analogizes his situation to voluntary intoxication in specific intent crimes. We are not persuaded to adopt the physical/mental distinction. Even if the brain is a “physical” organ reposing in the skull, it is nevertheless responsible for the vast majority of “mental” difficulties. Furthermore, there is authority that a “voluntary intoxication” theory must be noticed under Rule 12.2(b). See United States v. Olson, 576 F.2d 1267, 1273 (8th Cir.) (notice of defense of alcoholism required where defense would be used to negate intent element), cert. denied, 439 U.S. 896, 99 S.Ct. 256, 58 L.Ed.2d 242 (1978).
It is less clear, however, that the letter in question did not serve as adequate notice. The rule requires such notice to be given within the period for the filing of pre-trial motions. Fed.R.Crim.P. 12.2(b); see also Fed.R.Crim.P. 12.2(d) (court may exclude testimony for failure to give notice required by Rule 12.2(b)). Motions were due on February 5, 1988. Bernesser did not notify the government until August, however. The rule authorizes the court, “for cause shown,” to allow late notice or grant a continuation to permit the parties to prepare the new evidence for trial. Fed. R.Crim.P. 12.2(b). Rule 12.2(b) thus places the burden on the party seeking to submit late notice to move the court for a ruling as to good cause. Bernesser did not do so here. Counsel asserted at trial only that the letter had been sent out of an “abundance of caution,” because Bernesser’s position then as now was that notice was not required at all under the circumstances. This does not, of course, explain, much less excuse, the six month delay in sending it, and we cannot say that it was an abuse of discretion for Chief Judge Platt to have excluded the testimony in question. Cf. United States v. Duggan, 743 F.2d 59, 80 (2d Cir.1984) (finding no abuse of discretion where defendant failed to give timely notice as required by Fed.R.Crim.P. 12.2(a)).
Bernesser also couches his argument in terms of his Sixth Amendment right to present all evidence in his favor at his trial. We do not believe, however, that the Sixth Amendment is encroached upon by a discretionary, if strict, enforcement of the Federal Rules of Criminal Procedure. See Taylor v. Illinois, 484 U.S. 400, 108 5.Ct. 646, 653, 98 L.Ed.2d 798 (1988) (procedural rules for adversary process limit defendant’s right to present exculpatory evidence). Bernesser was seeking to introduce testimony of which he had been aware since 1987. His failure to assure its admissibility by timely notice is inconsistent with the crucial significance he now ascribes to it.
6. Taft-Hartley and the Minority Coalition
Cummings and DiBernardo attack their labor bribery-related convictions arising from the Cunningham Park minority coalition situation. Cummings was convicted of the Section 371 conspiracy along with DiBernardo, who was also convicted of the substantive bribe. They assert that their payments to Earl Ferguson, head of the Queens Minority Association, are not criminalized by the section of the Taft-Hartley Act under which they were charged. We reverse on related grounds.
This case went to trial with three counts in the indictment relating to the Cunningham Park affair. Count 85 charged Cummings and DiBernardo with delivering bribe money to Cervone. Count 86 charged them with aiding and abetting Cervone in the latter’s relay of the money to Ferguson. Both of these counts were charged under 29 U.S.C. § 186(a)(2). Count 83 charged a conspiracy to carry out the bribe to Ferguson, “a coconspirator,” by bribing Cervone. Cummings was convicted only on the conspiracy. DiBernardo was convicted on all three of the counts, but Count 86 was dismissed before sentencing.
Appellants argue that the evidence presented against them concerned only a payoff to Ferguson, not an independent attempt to influence Cervone. The statute under which appellants were charged prohibits employers from paying “any money or other thing of value ... to any labor organization, or any officer or employee thereof, which represents, seeks to represent, or would admit to membership, any of the employees of such employer.” 29 U.S.C. § 186(a)(2). Appellants argue stren[347]*347uously that Ferguson did not represent employees of Benjamin Corp., Cadin Corp., or DiBernardo Contracting, and that his Queens Minority Association was not a labor organization.
Ferguson’s status or that of his organization seems irrelevant, however, because the only substantive crime concerning the Cunningham Park project that is in the case, after the dismissal of Count 86, does not even mention Ferguson. The government concedes that Cervone gave the entire payment discussed in Count 85 to Ferguson and did not himself realize any tangible value out of the bribe. It argues instead that Cervone received the intangible value of a continuing ability to influence corrupt union practices. We are not persuaded.
The statute’s language speaks of a “thing of value” or “money,” clearly indicating that tangible items or at least valuable services or entitlements were contemplated. The government cites no caselaw to support its intangible benefit theory, and we are aware of none. There have been convictions under the statute for transfers to a friend or relative of the representative at the behest of the representative, see, e.g., United States v. Carlock, 806 F.2d 535, 555 (5th Cir.1986) (business benefit to representative’s daughter-in-law), cert. denied, 480 U.S. 949, 107 S.Ct. 1611, 94 L.Ed.2d 796 (1987); United States v. DeBrouse, 652 F.2d 383, 387-88 (4th Cir.1981) (payments to nominee of representative); United States v. Lanni, 466 F.2d 1102, 1107-09 (3d Cir.1972) (payments to representative’s girlfriend), but this is not such a case. Moreover, it is anything but clear what intangible benefit Cervone received, and that benefit thus seems not only intangible but also unidentifiable. We decline to adopt such a formless interpretation of this criminal statute, particularly since the payoff to Ferguson seemingly could have been prosecuted under a proper indictment.7
The conspiracy conviction in Count 83 must also be reversed as to both Cummings and DiBernardo. It alleges a conspiracy to commit the Ferguson bribe in Count 86 as well as the payment to Cer-vone in Count 85. One count was dismissed, and we have discussed above the defects of the other. It is immaterial that the conspiracy count also charged the bribe to Cervone under 18 U.S.C. § 1954. Cer-vone simply did not retain the money, and the payment to Ferguson was not for Cer-vone’s benefit. For the foregoing reasons, DiBernardo’s convictions on both counts and Cummings’ conviction on the Cunningham Park conspiracy count must be reversed.
Affirmed in part and reversed in part.