LUMBARD, Circuit Judge:

Lewis Novod petitions this court for a rehearing following our decision filed on January 17, 1991. United States v. Novod, 923 F.2d 970 (2d Cir.1991). We reversed Novod’s convictions for mail and wire fraud but affirmed his conspiracy and perjury convictions. We grant Novod’s petition for a rehearing, and reverse the conspiracy conviction and affirm the perjury *728 convictions. The judgment as to the mail and wire fraud convictions remains unchanged.

The fraud and conspiracy convictions were based on Novod’s participation in a scheme by Frank Sacco and Frank Amen-to to obtain a state dumping permit under false pretenses. The evidence at trial established that Novod, an attorney, helped conceal from the New York State Department of Environmental Conservation (NYS-DEC) that Sacco and Amento controlled a corporate applicant, Disposal Enterprise Corp. (DEC), for a permit to operate a dumpsite. After trial, Novod appealed his convictions on seven counts of wire fraud, and one count of conspiracy. We reversed the mail and wire fraud convictions pursuant to United States v. Schwartz, 924 F.2d 410 (2d Cir.1991), which held that a permit to export goods was not “property” within the meaning of the mail and wire fraud statutes. 18 U.S.C. §§ 1341, 1343 (1988). In light of our disposition of the mail and wire fraud counts, Novod argues that the conspiracy and perjury convictions should also be reversed.

In submitting the conspiracy count to the jury, Judge Broderick gave the following instruction:

The first element, that there was a conspiratorial agreement, and in this case that is an agreement to execute a scheme to obtain property, to wit, the permit to operate the Skibitsky property, and that that was an agreement between two or more persons.

Having held that the permit was not property within the meaning of the mail and wire fraud statutes, we now conclude that the conspiracy conviction should be reversed.

Novod argues that if we reverse the conspiracy conviction, we should remand for a new trial on the perjury counts because of the prejudicial “spillover” effect that evidence of the conspiracy had on the perjury counts. We disagree. Criminal suspects are frequently charged with multiple counts, some of which are dismissed on procedural grounds, dismissed for lack of evidence or which result in convictions that are reversed upon appeal. Federal Rule of Criminal Procedure 8(a) provides for join-der of offenses “if the offenses charged, ... are based on the same act or transactions connected together or constituting parts on a common scheme or plan.” Relief from prejudicial joinder of offenses is required by Fed.R.Crim.P. 14. Novod did not seek a severance of the perjury counts. To invoke “ ‘retroactive misjoinder,’ ” No-vod must show “ ‘compelling prejudice,’ ” Callanan v. United States, 881 F.2d 229, 236 (6th Cir.1989), cert. denied, — U.S. -, 110 S.Ct. 1816, 108 L.Ed.2d 946 (1990) (quoting United States v. Warner, 690 F.2d 545, 554 (6th Cir.1981)).

Novod has not shown “compelling prejudice.” The evidence of conspiracy to defraud the state of New York, as the district court held, was admissible to prove the perjury charges. The statute proscribing perjury before a grand jury, 18 U.S.C. § 1623 (1988), requires false statements before a grand jury to be made “knowingly.” Evidence of the conspiracy to conceal Ar-mento’s and Sacco’s interests in DEC from the NYSDEC helped establish that Novod knew his denials of such knowledge before the grand jury were false.

Novod contends that even if the conspiracy evidence is admissible on the perjury counts, we should remand for a new trial because the trial court did not perform on-the-record-balancing tests before admitting that evidence. Although the district court did not expressly balance the probative value of the conspiracy evidence against its prejudicial impact, see Fed.R.Evid. 403, we have held that a “ ‘mechanical recitation of Rule 403’s formula as a prerequisite to admitting evidence’ is not required.” United States v. Sliker, 751 F.2d 477, 487 (2d Cir.1984) (quoting United States v. Sangrey, 586 F.2d 1312, 1315 (9th Cir.1978)), cert. denied, 470 U.S. 1058, 105 S.Ct. 1772, 84 L.Ed.2d 832, 471 U.S. 1137, 105 S.Ct. 2679, 86 L.Ed.2d 697 (1985) (citations omitted). We believe it is implicit in the district court’s ruling that the probative value of Novod’s participation in concealing the interests of Sacco and Armento in DEC outweighed its prejudicial impact. We see no error in that ruling.

*729 Novod also argues that his false testimony did not satisfy the materiality requirement of § 1623 because the scheme of artifice being investigated by the grand jury did not constitute a federal offense. The legitimate scope of the grand jury’s inquiry extends to “any evidence which may afford valuable leads for investigation of suspected criminal activity during the limitations period.” United States v. Cohn, 452 F.2d 881, 883 (2d Cir.1971), cert. denied, 405 U.S. 975, 92 S.Ct. 1196, 31 L.Ed.2d 249 (1972). As we stated in United States v. Doulin, 538 F.2d 466, 470 (2d Cir.), cert. denied, 429 U.S. 895, 97 S.Ct. 256, 50 L.Ed.2d 178 (1976):

Appellant’s claim that neither federal grand jury before which he appeared had authority to indict him for the substantive offenses about which he has now been found guilty of lying is, even if true, beside the point. The grand jury’s duty and indeed responsibility to inquire is not coterminous with its power to indict.

Regardless of whether we employ the more stringent definition of materiality of United States v. Freedman, 445 F.2d 1220, 1227 (2d Cir.1971) (“truthful answer would have been of sufficient probative importance to the inquiry so that, as a minimum, further fruitful investigation would have occurred”) (emphasis supplied), or of United States v. Mancuso, 485 F.2d 275, 280-81 (2d Cir.1973) (“truthful answer could conceivably have aided the grand jury investigation”) (emphasis supplied), 1 we find that Novod’s interrogation before the grand jury was material to the grand jury’s investigation of racketeering offenses committed by Sacco and Armento. Consequently, Novod’s testimony was subject to the sanctions for perjury.

During the course of his two grand jury appearances, Novod repeatedly denied any knowledge of Sacco’s and Armento’s hidden interest in DEC, a fact which had been concealed from NYSDEC while DEC applied for a permit to operate a dumpsite. Truthful answers would have furthered the grand jury’s investigation of illegal dumping by Sacco and Armento, who were eventually convicted of federal racketeering crimes. In addition, the grand jury was also investigating the possibility that No-vod had violated 18 U.S.C. § 1962 (1988) (proscribing investment of income derived from a pattern of racketeering activities). Therefore, Novod’s testimony before the grand jury was material for the purposes of § 1623.

Novod also argues that this case should be remanded tor a resentencing hearing so that he may avail himself of the two-level offense reduction for acceptance of responsibility allowed by Federal Sentencing Guidelines Section 3E1.1. We disagree. Novod is not entitled to resentenc-ing. Although Novod raised legal challenges to the validity of the mail and wire fraud and conspiracy charges, he made no such challenge to the perjury charges. Nothing prevented him from demonstrating “a recognition and affirmative acceptance of personal responsibility” for his false grand jury testimony. Novod never acknowledged his participation in the scheme to conceal Sacco’s and Armento’s interest in DEC.

In addition, there is no reason to Deneve tnat me aistrict court wouia nave given Novod a different sentence absent the mail and wire fraud and conspiracy convictions. Judge Broderick was aware of the possibility that McNally v. United States, 483 U.S. 350, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987), might warrant reversal of those convictions on appeal, yet the seriousness of the perjury charges compelled him to sentence Novod to ten months of incarceration, to run concurrently with sentences from the other convictions. Thus, remand for resentencing is unnecessary.

Affirmed in part and Reversed in part.

Notes

. In United States v. Demauro, 581 F.2d 50, 53, n. 1 (2d Cir.1978), we expressly left open the question of which standard applies in the context of a grand jury investigation. We do not resolve that question because we find that Nc vod’s misstatements were material under eithe standard.