Defendant Richard Foley, Jr., a state legislator, appeals from a judgment entered in the United States District Court for the District of Connecticut convicting him, following a jury trial before T.F. Gilroy Daly, Judge, on one count of accepting a bribe, in violation of 18 U.S.C. § 666(a)(1)(B) (1988); two counts of filing a false income tax return, in violation of 18 U.S.C. § 7206(2) (1988); and one count of conspiring to file a false income tax return, in violation of 18 U.S.C. § 371 (1988). Foley was sentenced principally to 40 months’ imprisonment, to be followed by a three-year term of supervised release, and was fined $25,000. On appeal, he contends that his convictions should be reversed because (a) the bribery conduct alleged and proven was not within the scope of § 666(a)(1)(B), and (b) the verdicts on the *486tax-related counts were dependent on the validity of his conviction on the bribery count. For the reasons stated below, we agree that the proven transaction was not shown to be within the scope of § 666(a)(1)(B); the conviction on the bribery count must therefore be reversed and that count dismissed. We conclude that the convictions on the tax-related counts, because they may have resulted from the invalid verdict on the bribery count, must be vacated and those counts remanded for further proceedings.
I. BACKGROUND
The present prosecution charged that Foley, a member of the Connecticut General Assembly’s House of Representatives, accepted payments in exchange for agreeing to influence certain legislation. Among the government’s witnesses at trial were real estate developers Richard Barbieri, Sr., and John Corpaci, who had pleaded guilty to, inter alia, bank fraud and political corruption. They testified that they made the corrupt payments to Foley and that Foley provided them with fraudulent receipts in order to facilitate their deduction of the payments as business expenses. Taken in the light most favorable to the government, the evidence showed the following.
In 1989, Barbieri, Corpaci, and Vinal S. Duncan, through their Taft-Crosspointe Limited Partnership (“Taft>-Crosspointe” or the “Partnership”), planned to develop a shopping plaza in Naugatuck, Connecticut, and sought a $12,500,000 loan for that purpose from Fleet Bank (“Fleet”). Fleet owned United Bank and Trust (“UBT”), but it had merged with Norstar Bank and thus was required, under Connecticut law, to divest itself of UBT promptly after the merger. Fleet was attempting, however, to obtain from the state legislature a delay of the divestiture requirement. Fleet informed Barbieri and Corpaci that a proposed one-year exemption had been defeated in the Connecticut General Assembly and that a majority of those voting against it were Republicans. Fleet asked Barbieri, who was active in Republican politics, and Corpaci to contact legislators who might be able to assist in having the proposal reconsidered.
Foley, a Republican and long-time acquaintance of Barbieri, was a member of the General Assembly’s Banking Committee. Barbi-eri and Corpaci contacted Foley in an effort to help Fleet. During their conversation, Foley said he could not change his own vote on the exemption proposal because he had been so openly opposed, but he indicated that he could deliver the necessary votes from others. In exchange, Foley asked to be hired as a consultant for Taft-Crosspointe at a salary of $2,500 a month. Barbieri and Corpaci, who on numerous prior occasions had agreed to make payments to public officials in exchange for political favors, agreed. Thus, Taft-Crosspointe would pay Foley monthly, and Foley would send invoices that would enable the Partnership to deduct those amounts on tax returns as a business expense. It was agreed that Foley would contact several people so as to permit the Partnership to claim that Foley was soliciting business for it and provide an explanation for the payments to him if the three men were ever questioned; however, their understanding was that the payments were made in return for Foley’s assistance on the Fleet legislation rather than for any consulting work.
The Connecticut General Assembly thereafter reconsidered the exemption requested by Fleet and, on reconsideration, passed the legislation. Foley submitted to the developers invoices listing charges for “tenant solicitation” or the like, which were paid by Taft-Crosspointe or by Taft Group, another entity owned by the developers. In fact, Foley did not provide any services to Taft-Crosspointe or Taft Group other than in connection with the banking exemption, but he received from them payments totaling $25,000.
In 1993, Foley was indicted on charges (a) that his acceptance, as “an agent of state government” (Indictment ¶20), of money with the intent to be influenced with regard to the proposed exemption legislation in the Connecticut General Assembly violated 18 U.S.C. § 666(a)(1)(B) (count 1) (the “bribery count”); and (b) that his submission of false invoices aided in the preparation of false tax *487returns for Taft-Crosspointe and Taft Group, in violation of 26 U.S.C. § 7206(2) (counts 2 and 3, respectively), and furthered a conspiracy to violate the federal tax laws, in violation of 18 U.S.C. § 371 (count 4) (collectively the “tax-fraud” counts).
The bribery count charged, in pertinent part, that Foley had
knowingly, willfully, and corruptly solicited, demanded for his benefit, accepted, and agreed to accept things of value, that is, checks in the total amount of $25,000, from Richard D. Barbieri, Sr. and John A. Corpaci, acting through and on behalf of the Taft Group, intending to be influenced and rewarded in connection with the business and transactions of Connecticut state government involving a thing of value of $5,000 or more, that is, a legislative exemption to the divestiture provisions of the state’s Interstate Banking Law.
(Indictment ¶23.) One of Fleet’s attorneys testified that because of the cost of selling UBT, the exemption was worth substantially more than $5,000 to Fleet. The evidence did not show what value, if any, the one-year’s difference had to the State of Connecticut.
The trial court instructed that, in order to return a verdict of guilty on the bribery count, the jury must first find “that Richard Foley was an agent, official or representative of a state government at the time of the alleged offense,” and it advised the jury that “[a] state legislator is an agent of a state government for the purposes [of] this element.” (Trial Transcript dated October 28, 1993 (“October 28 Tr.”), at 81-82.) The court also instructed the jury that the government was required to prove, inter alia, that Foley had accepted something of value in connection with a business or transaction of the state government involving anything having a value of $5,000 or more. As to the latter requirement, the court instructed the jury that “it is not necessary for the transaction or transactions by the state government actually to have involved any federal funds received by the state” and stated that this element was otherwise “self-explanatory.” (Id. at 83.)
As to the tax-fraud counts, the court charged the jury, inter alia, that an income tax return is false or fraudulent if the taxpayer’s income is understated or its deductions are overstated, that deductions from gross income are lawful only for legitimate items and expenses, and that “[m]oney paid to a public official for a corrupt purpose is not a legitimate expense and a taxpayer is not allowed to deduct such payments as business expenses.” (Id. at 93.)
The jury found Foley guilty on all counts, and he was sentenced as indicated above. This appeal followed.
II. DISCUSSION
On appeal, Foley contends principally that the conduct with which he was charged and which was proven at trial does not constitute a violation of § 666(a)(1)(B) because (1) the value to Fleet of the exemption under the banking law was not shown to be a proper measure of value for purposes of that provision, and (2) a state legislator is not an “agent” within the meaning of the statute. We agree with his first contention and hence need not reach the second. Foley also contends that the tax-fraud convictions cannot be upheld because they were premised on the flawed bribery conviction. Since we cannot be sufficiently certain that the tax-fraud convictions were not based on the flawed bribery conviction, we conclude that they should be vacated and those counts retried.
Preliminarily, we address the government’s contention that we should not entertain the above challenges to the bribery conviction because Foley failed to make them in the district court. Although some claims of error may be forfeited by the failure to make timely objection, see, e.g., United States v. Olano, 507 U.S. 725, 730-32, 113 S.Ct. 1770, 1776, 123 L.Ed.2d 508 (1993); Yakus v. United States, 321 U.S. 414, 444, 64 S.Ct. 660, 677, 88 L.Ed. 834 (1944), others are so fundamental that an appellate court will review them despite the fact that they have not been raised below. For example, an appellate court that sees that the lower court proceeded without subject matter jurisdiction must correct the error even if neither party brought it to the lower court’s attention. See, e.g., Bender v. *488Williamsport Area School District, 475 U.S. 534, 541, 106 S.Ct. 1326, 1331, 89 L.Ed.2d 501 (1986). In a criminal case, a “failure of the indictment to charge an offense may be treated as [a] jurisdictional” defect, United States v. Doyle, 348 F.2d 715, 718 (2d Cir.), cert. denied, 382 U.S. 843, 86 S.Ct. 89, 15 L.Ed.2d 84 (1965); see also United States v. Meacham, 626 F.2d 503, 509-10 (5th Cir.1980) (objection that indictment failed to charge an offense is not waived by a guilty plea), cert. denied, 459 U.S. 1040, 103 S.Ct. 455, 74 L.Ed.2d 608 (1982), and an appellate court must notice such a flaw even if the issue was raised neither in the district court nor on appeal. See Fed.R.Crim.P. 12(b)(2); United States v. Ivic, 700 F.2d 51, 59 n. 5 (2d Cir.1983), questioned on other grounds, National Organization for Women, Inc. v. Scheidler, — U.S. -, -, 114 S.Ct. 798, 805, 127 L.Ed.2d 99 (1994). Issues that go to whether the conduct alleged and proved is punishable under the statute charged are thus cognizable on appeal under the plain-error doctrine.
In assessing whether the indictment charges an offense under the statutory provision alleged, we note that “[i]t is generally sufficient that an indictment set forth the offense in the words of the statute itself, as long as ‘those words of themselves fully, directly, and expressly, without any uncertainty or ambiguity, set forth all the elements necessary to constitute the offence intended to be punished.’ ” Hamling v. United States, 418 U.S. 87, 117, 94 S.Ct. 2887, 2907, 41 L.Ed.2d 590 (1974) (quoting United States v. Carll, 105 U.S. 611, 612, 26 L.Ed. 1135 (1881)). When, however, one element of the offense is implicit in the statute, rather than explicit, and the indictment tracks the language of the statute and fails to allege the implicit element explicitly, the indictment fails to allege an offense. See id. at 613 (indictment that failed to allege that the defendant knew an uttered document was forged failed to charge a crime although statute did not make the knowledge element explicit); United States v. Ivic, 700 F.2d at 58-59, 64-65 (where indictment tracked the language of RICO statute but did not allege economic motivation, which was an essential characteristic of the crime, the indictment failed to charge an offense).
Foley contends that the reference in § 666(a)(1)(B) to a thing “of value of $5,000 or more” implicitly refers to its value to a recipient of federal program funds, and that the indictment alleged no more than that he influenced a transaction that had that value to Fleet, a private entity that was not shown to either receive or control federal program funds. Thus, his challenge to his bribery conviction includes a contention that count one of the indictment failed to allege (and that the government’s trial evidence failed to prove) an offense within the scope of the statutory section under which he was charged and convicted. We conclude that this challenge may be entertained under the plain-error doctrine.
A. The Bribery Conviction under § 666(a)(1)(B)
Section 666(a)(1)(B) provides, in pertinent part, as follows:
§ 666. Theft or bribery concerning programs receiving Federal funds
(a) Whoever, if the circumstance described in subsection (b) of this section exists—
(1) being an agent of an organization, or of a State, local, or Indian tribal government, or any agency thereof—
(B) corruptly solicits or demands for the benefit of any person, or accepts or agrees to accept, anything of value from any person, intending to be influenced or rewarded in connection with any business, transaction, or series of transactions of such organization, government, or agency involving anything of value of $5,000 or more;
shall be fined under this title, imprisoned not more than 10 years, or both.
(b) The circumstance referred to in subsection (a) of this section is that the organization, government, or agency receives, in any one year period, benefits in excess of $10,000 under a Federal program involving a grant, contract, subsidy, loan, guar*489antee, insurance, or other form of Federal assistance.
18 U.S.C. §§ 666(a)(1)(B) and (b) (as amended in 1986, see Criminal Law and Procedure Technical Amendments Act of 1986, Pub.L. No. 99-646, § 59, 100 Stat. 3592, 3612-13 (1986) (making “technical” amendments); H.R.Rep. No. 797, 99th Cong., 2d Sess. 30 (1986), reprinted in 1986 U.S.Code Cong. & Admin.News (“USCCAN”) 6138, 6153).
As the terms of §§ 666(a)(1)(B) and 666(b) make plain, not all bribe-taking by an agent of the state falls within the scope of § 666. A state agent who accepts a bribe violates this section only if (a) the state receives federal program benefits in excess of $10,000 in a one-year period, and (b) the bribe is accepted in connection with a state business or a state transaction or series of transactions “involving anything of value of $5,000 or more.” While § 666(b) specifies that the more-than-$10,000 in federal program benefits must have been received by the organization, government, or agency of which the defendant is an agent, § 666(a)(1)(B) is silent as to the identity of the person or entity to whom the “[]thing” must have at least a $5,000 value. Accordingly, we look to the legislative history and purpose of the statute for illumination. See generally Dowling v. United States, 473 U.S. 207, 213, 105 S.Ct. 3127, 3131, 87 L.Ed.2d 152 (1985) (court must “pay close heed to language, legislative history, and purpose in order strictly to determine the scope of the conduct the enactment forbids”).
1. The Legislative History
The legislative history of § 666, which was introduced as part of Title XI of the Compre-1-hensive Crime Control Act of 1984, indicates that the section was enacted in an attempt to increase the protection of the integrity of federal funds disbursed through federal programs. Prior to 1984, it was a federal offense to steal property of the United States, see 18 U.S.C. § 641; it was also a federal offense for an officer or employee of an agency receiving assistance under the Comprehensive Employment Training Act (“CETA”) or the Job Training Partnership Act to, inter alia, steal funds administered thereunder or to demand a bribe in connection with the granting of a job-training contract, see 18 U.S.C. § 665; and it was a federal offense for a federal .public official corruptly to, inter alia, accept anything of value personally in return for being influenced in the performance of an official act, see, e.g., 18 U.S.C. § 201. Section 641, however, did not reach thefts of federal property after title or control had passed from the United States to the federal program recipient, see, e.g., United States v. Morris, 541 F.2d 153, 155 (6th Cir.1976); see also United States v. Benefield, 721 F.2d 128, 129-30 n. 2 (4th Cir.1983) (citing cases); by its terms, § 665 dealt only with the job-training programs, not with the myriad other programs receiving federal financial assistance; and the courts of appeals had divided over the question of whether and under what circumstances § 201 reached individuals not employed by the federal government, compare, e.g., United States v. Mosley, 659 F.2d 812 (7th Cir.1981) (state administrator covered), with United States v. Del Toro, 513 F.2d 656 (2d Cir.) (municipal administrator not covered), cert. denied, 423 U.S. 826, 96 S.Ct. 41, 46 L.Ed.2d 42 (1975).
Section 666 was enacted in an effort to fill these gaps. The Report of the Senate Judiciary Committee explaining the proposed § 666 stated that the section was
designed to create new offenses to augment the ability of the United States to vindicate significant acts of theft, fraud, and bribery involving Federal monies that are disbursed to private organizations or State and local governments pursuant to a Federal program.
S.Rep. No. 225, 98th Cong., 2d Sess. 369 (1984) (“Senate Report” or “Report”), reprinted in 1984 USCCAN 3510. In describing the then-existing state of the law, the Senate Report stated in part as follows:
... title XI covers both theft and bribery type offenses. With respect to theft, 18 U.S.C. 665 makes theft or embezzlement by an officer or employee of an agency receiving assistance under the Job Training Partnership Act a Federal offense. However, there is no statute of general applicability in this area, and thefts from *490other organizations or governments receiving Federal financial assistance can be prosecuted under the general theft of Federal property statute, 18 U.S.C. 641, only if it can be shown that the property stolen is property of the United States. In many cases, such prosecution is impossible because title has passed to the recipient before the property is stolen, or the funds are so commingled that the Federal character of the funds cannot be shown. This situation gives rise to a serious gap in the law, since even though title to the monies may have passed, the Federal Government clearly retains a strong interest in assuring the integrity of such program funds.
Senate Report at 369, 1984 USCCAN at 3510. The Report also noted the existence of “doubt as to whether or under what circumstances persons not employed by the Federal Government” could be prosecuted under § 201, Senate Report at 369, 1984 USCCAN at 3510, and indicated that § 666 was intended to reach the conduct of state and local officials such as the administrators in United States v. Mosley, 659 F.2d 812 (bribery in connection with administration of CETA program), and United States v. Del Toro, 513 F.2d 656 (bribery in connection with federally funded program’s leasing of office space); see Senate Report at 370 n. 3,1984 USCCAN at 3511 n. 3. Thus, § 666 was intended to be a law of general application to safeguard federal funds distributed through federal programs, and was designed to permit prosecution for, inter alia, theft, see 18 U.S.C. § 666(a)(1)(A), and bribery, see id. § 666(a)(1)(B), in connection with those funds even after title had passed from the federal government, and to reach not only federal employees, but also, inter alios, employees of the state.
In describing the details of the proposed § 666, the Senate Report noted, however, that although § 666’s protection of certain federal funds is very broad, this protection extends only to a very specific federal interest, namely, safeguarding the integrity of federal funds that are intended to serve legislatively defined policy objectives:
The Committee intends that the term “Federal program involving a grant, a contract, a subsidy, a loan, a guarantee, insurance, or another form of Federal assistance” be construed broadly, consistent with the purpose of this section to protect the integrity of the vast sums of money distributed through Federal programs from theft, fraud, and undue influence by bribery. However, the concept is not unlimited. The term “Federal program” means that there must exist a specific statutory scheme authorizing the Federal assistance in order to promote or achieve certain policy objectives. Thus, not every Federal contract or disbursement of funds would be covered.
Senate Report at 370,1984 USCCAN at 3511 (emphasis added).
In sum, the legislative history of § 666 indicates that the value of a thing for purposes of § 666(a)(1)(B) is not to be assessed by reference to any and every perspective or measure of value, no matter how subjective or arbitrary. Instead, the assessment of the thing’s value must be connected, even if only indirectly, to the integrity of federal program funds.
2. Judicial Interpretation of § 666
Consistent with Congress’s desire to safeguard federal funds, including those that may have become so commingled that their federal character cannot be shown, this Court has held that in order to establish the more-than-$10,000 jurisdictional amount set out in § 666(b), the government need not trace the federal funds received by an organization to the project in connection with which its employee received a bribe. See United States v. Coyne, 4 F.3d 100, 108-10 (2d Cir.1993), cert. denied, — U.S. -, 114 S.Ct. 929, 127 L.Ed.2d 221 (1994). In Coyne, the defendant was a county official accused of, inter alia, taking a bribe in connection with the construction of a county civic center. Although the county received federal funds, it received none that were earmarked for the civic center, and Coyne argued that the more-than-$10,000 jurisdictional amount set out in § 666(b) was therefore not met. We rejected this argument, stating as follows:
The statutory language of Section 666 requires proof only that the accused be an *491agent of a local government that received in excess of $10,000 of federal funds in the one year period. The language neither explicitly nor implicitly requires that the $10,000 be directly linked to the program that was the subject of the bribe.
4 F.3d at 109.
In a similar effort to honor Congress’s objective of protecting federal program funds even when their federal character is difficult to show, other Circuits have ruled that the government has no burden to trace the funds with respect to § 666(a)(l)(B)’s requirement that the “[jthing” have a value of at least $5,000. In United States v. Westmoreland, 841 F.2d 572 (5th Cir.), cert. denied, 488 U.S. 820, 109 S.Ct. 62, 102 L.Ed.2d 39 (1988), for example, the court stated that
while the legislative history manifests a congressional intent to preserve the integrity of federal funds, Congress specifically chose to do so by enacting a criminal statute that would eliminate the need to trace the flow of federal monies and that would avoid inconsistencies caused by the different ways that various federal programs disburse funds and control their administration.
Id. at 577. Noting that the subsection that establishes the “$5,000 or more” requirement does not mention federal funds, the court upheld the § 666 conviction of a county supervisor for taking bribes in connection with the granting of contracts for the maintenance of local roads and bridges although the funds corruptly disbursed were not shown to be federal funds. The court stated that “it is clear that Congress has east a broad net to encompass local officials who may administer federal funds, regardless of whether they actually do.” United States v. Westmoreland, 841 F.2d at 574-75, 577; see also United States v. Simas, 937 F.2d 459, 463 (9th Cir.1991) (“By enacting section 666, Congress plainly decided to protect federal funds by preserving the integrity of the entities that receive the federal funds rather than requiring the tracing of federal funds to a particular illegal transaction.”); United States v. Snyder, 930 F.2d 1090, 1091-93 (5th Cir.), cert. denied, 502 U.S. 942, 112 S.Ct. 380, 116 L.Ed.2d 331 (1991).
This Court, in dealing with the $5,000 requirement, has held that § 666(a)(1)(B) was applicable where an employee of an organization that, received the requisite more-than-$10,000 in federal program funds accepted a bribe in exchange for attempting, in a joint operation between his organization and another that apparently was not shown to meet the more-than-$10,000 requirement, to cause the expenditure of $5,000 or more by the other organization. See United States v. Bonito, 57 F.3d 167 (2d Cir.1995). In Bonito, the defendant, a landlord and real estate developer, was charged with giving a bribe to one DeMatteo, who was, inter alia, Director of Real Estate Services for the City of New Haven, Connecticut (the “City”). The New Haven Housing Authority was an agency independent of the City, established by the state to select sites for low-income housing in the City and to administer projects funded by the federal Department of Housing and Urban Development (“HUD”). A joint committee of the City and the Housing Authority was established to recommend such sites. The Mayor of New Haven directed that no site be accepted without his prior approval and appointed DeMatteo to serve on the joint committee as his agent. After receiving an automobile from Bonito, DeMatteo attempted, unsuccessfully, to persuade HUD to allow the Housing Authority to purchase one of Bonito’s housing developments. Prosecuted under § 666, Bonito challenged the government’s proof that the proposed purchase involved a thing having the value of $5,000 or more within the meaning of § 666(a), arguing that, although the City itself received more than $10,000 in federal funds, the proposed purchaser of his development, whose expenditure would be $5,000 or more, was to be the Housing Authority, which was an agency independent of the City. Thus, he argued that “there [wa]s no connection between the corrupted business or transaction and the protection of federal funds.” 57 F.3d at 172. Though acknowledging the closeness of the question, we rejected this argument, stating as follows:
[TJhere are a number of factors in favor of construing § 666 to cover corruption of agents- of a federally funded organization *492even in those official activities that do not implicate their organization’s own funds.... [T]he statute does not say that the thing of value of $5,000 must be that of the affected organization. It says only that the corruption must be in connection with the organization’s business or transaction “involving” a thing of value of $5,000 or more. In addition, we have already extended the statute beyond corruption in a local organization’s administration of a federally funded program. United States v. Coyne, 4 F.3d at 110. The rationale for this was stated most succinctly by the Fifth Circuit: “It is sufficient that Congress seeks to preserve the integrity of federal funds by assuring the integrity of the organization that receives them.” United States v. Westmoreland, 841 F.2d [at 578].
United States v. Bonito, 57 F.3d at 172. We concluded that since the determination of the location of low-income housing was a “joint enterprise ... that would determine the disposition of federal grant monies,” id. at 173, the corruption of an official of one member of the enterprise to influence the disposition of federal funds by the other member was within the purview of § 666.
This conclusion does no violence to the actual words of the statute, and, based on the unusual fact that federal funds were sought to be corrupted through the Housing Authority, serves the statute’s underlying purpose. It would be quite another case if the corrupted business affected neither the financial interests of the protected organization nor, as in this case through the Housing Authority, federal funds directly.
57 F.3d at 173.
In United States v. Rooney, 37 F.3d 847 (2d Cir.1994), we dealt with the § 666 prosecution of a defendant who had formed a partnership for the development of a housing project for the elderly, funded by a federal agency, the Farmers Home Administration (“FmHA”). At a time when costs were mounting, Rooney, who was personally obligated on the partnership’s debts both to the contractor and to FmHA, offered to borrow more from the agency and pay the contractor immediately if the contractor would, subject to FmHA approval, install a pond adjacent to the development at no additional cost to the project. After discussing the legislative history of § 666(a)(1)(B), see 37 F.3d at 851-52 (“as is evident from the circumstances surrounding its adoption, § 666’s manifest purpose is to safeguard finite federal resources from corruption and to police those with control of federal funds”), and noting that Rooney was a private individual rather than a public official, and that “the only government favor that Rooney had within his control to dole out was the proceeds of a FmHA loan upon which he himself would remain liable,” id. at 850, we concluded, inter alia, that the Congressional concern underlying the enactment of § 666, i.e., the preservation of federal funds, was not implicated by Rooney’s conduct, see id. at 854. We also noted that the choice proffered by Rooney to the contractor could be viewed as an ordinary business transaction, which § 666(a)(1)(B) was not meant to encompass.
In sum, we have held that in order to establish an offense under § 666(a)(1)(B), the government is not required to trace the agent’s corrupt expenditures to the federal program funds; but we have held that there was no violation of that section where the preservation of federal funds was not implicated by the defendant’s conduct; and we have expressed doubt as to whether § 666(a)(1)(B) would be applicable where the conduct at issue affects neither the federal program funds received by a protected organization nor the receiving organization’s financial interests.
3. The Present Case
In the present case, the government presented evidence to show that, without the legislative exemption, Fleet would have been required to divest itself of UBT promptly and that selling off UBT would have cost Fleet substantially more than $5,000. Thus, the jury could have concluded that the exemption enacted by the Connecticut legislature had a value of more than $5,000 to Fleet. Fleet, however, was a private entity, and no evidence was presented that it received federal funds or that it had any role, *493direct or indirect, in administering or recommending the expenditure of any federal program moneys. Though it is undisputed that the State of Connecticut, during the pertinent period, was a recipient of more than $10,000 in federal assistance, the government did not show that the exemption legislation had any financial value to the State of Connecticut; nor did it show that the exemption had any connection whatever with a federal program. In short, insofar as the evidence presented in this case reveals, the exemption affected neither the financial interests of the protected organization nor federal funds directly.
Plainly some briberies of state officials may come within the scope of § 666(a)(1)(B), but we infer from the legislative history that that section was not designed for the prosecution of corruption that was not shown in some way to touch upon federal funds. Accordingly, we conclude that the government failed to prove that Foley was guilty of an offense under § 666(a)(1)(B), and his conviction on the bribery count must be reversed.
B. The Tax-Fraud Convictions
The question remains to what degree the invalid conviction under § 666(a)(1)(B) affected Foley’s tax-fraud conviction for assisting in the Taft-Crosspointe and Taft Group fraudulent overstatements of their deductions on their federal income tax returns. It is a federal offense willfully to assist in the preparation of a tax return “which is fraudulent or is false as to any material matter,” 26 U.S.C. § 7206(2), and a willful assistance in the taxpayer’s overstatement of its deductions is prosecutable under this provision. See, e.g., United States v. Owen, 15 F.3d 1528, 1530, 1535 (10th Cir.1994). A business is allowed to deduct the ordinary and necessary expenses of its operations, see 26 U.S.C. § 162(a) (1988), but it is not allowed to deduct as an ordinary and necessary business expense “any payment made, directly or indirectly, to an official or employee of any government ... if the payment constitutes an illegal bribe or kickback.” 26 U.S.C. § 162(c)(1) (1988) (emphasis added). This section allows for the possibility that some bribes or kickbacks may be lawful; if lawful, they may properly be deducted if they are ordinary and necessary expenses of the business. See Raymond Bertolini Trucking Co. v. Commissioner, 736 F.2d 1120, 1123-25 (6th Cir.1984) (concluding on facts of case that kickback was legal, ordinary, and necessary and hence was deductible); cf. Car-Ron Asphalt Paving Co. v. Commissioner, 758 F.2d 1132, 1133-34 (6th Cir.1985) (finding legal kickback not necessary and thus not deductible).
Further, the source of the illegality referred to in 26 U.S.C. § 162(c)(1) may be either federal or state law. See 26 U.S.C. § 162(c)(2); see also Commissioner v. Tellier, 383 U.S. 687, 693-94, 86 S.Ct. 1118, 1121-22, 16 L.Ed.2d 185 (1966). Thus, a properly instructed jury may convict under § 7206(2) based on the deduction of a bribe that was (a) illegal under federal law, (b) illegal under state law, or (c) legal but not an ordinary and necessary business expense. When, however, the jury has been presented with several bases for conviction, one of which is invalid as a matter of law, and it is impossible to tell which ground the jury selected, the conviction must be vacated. See, e.g., Yates v. United States, 354 U.S. 298, 312, 77 S.Ct. 1064, 1073, 1 L.Ed.2d 1356 (1957) (prosecution for conduct beyond statute-of-limitations period invalid as a matter of law), partially overruled on other grounds by Burks v. United States, 437 U.S. 1, 7-10, 98 S.Ct. 2141, 2145-47, 57 L.Ed.2d 1 (1978); Stromberg v. California, 283 U.S. 359, 368-70, 51 S.Ct. 532, 535-36, 75 L.Ed. 1117 (1931) (prosecution for constitutionally protected conduct invalid as a matter of law); see generally Griffin v. United States, 502 U.S. 46, 52-56, 112 S.Ct. 466, 470-73, 116 L.Ed.2d 371 (1991). Though the mere insufficiency of the evidence to support one of the bases submitted to the jury does not fall within this principle, see id. at 56, 112 S.Ct. at 472-73, a basis is invalid as a matter of law when the conduct in question “fails to come within the statutory definition of the crime,” id. at 59, 112 S.Ct. at 474; see, e.g., United States v. Musacchia, 955 F.2d 3, 4 (2d Cir.1991) (withdrawing earlier affirmance and remanding for new trial where, after affirmance, government raised inapplicability of substantive *494provision, and court could not determine whether or not that provision was basis for conspiracy conviction).
In the present case, the jury was presented with two bases on which it could find that Foley had willfully aided in the preparation of a tax return that was false as to a material matter. First, the indictment, which the judge read to the jury as part of its instructions, and which the jury had with it during its deliberations, alleged that Foley had assisted in the taxpayers’ deductions of the bribery payments, though they were “not a legitimate business expense.” This facet of the instructions permitted the jury to convict on the theory that bribe payments were not “ordinary and necessary” business expenses.
The second basis related to the impermis-sibility of a deduction for bribes that were illegal. In this connection, the district court instructed the jury that “[m]oney paid to a public official for a corrupt purpose is not a legitimate expense and a taxpayer is not allowed to deduct such payments as business expenses.” (October 28 Tr. at 93.) Assuming that use of the phrase “for a corrupt purpose” — a phrase that suggests a subjective test — was a sufficient surrogate for the objective requirement that the bribe or kickback be “illegal,” the court’s instruction appears plainly to have been premised on the bribery having come within the scope of § 666(a)(1)(B). There is no indication that the government invoked any provision of state law, such as Conn.Gen.Stat. § 53a-147 (1994), which provides that “[a] person is guilty of [the felony of] bribery if he promises, offers, confers or agrees to confer upon a public servant ... any benefit as consideration for the recipient’s decision, opinion, recommendation or vote as a public serv-ant_” See also id. § 58a-148 (1994) (“A public servant ... is guilty of [the felony of] bribe receiving if he solicits, accepts or agrees to accept from another person any benefit for, because of, or as consideration for his decision, opinion, recommendation or vote.”). The only basis for illegality presented to the jury was § 666(a)(1)(B).
Since we have concluded that the conduct alleged and proven with respect to the bribery count was not an offense under § 666(a)(1)(B), the only section under which Foley was charged with bribery, and since we are unable to determine whether the jury’s general verdict was based on the view that the bribe payments were not ordinary and necessary expenses or instead was based on the premise that the deduction was impermissible because the bribe payments were illegal under § 666(a)(1)(B), we vacate Foley’s convictions on the tax-fraud counts and remand for a new trial on those counts.
CONCLUSION
For the reasons stated above, the judgment of conviction on count one is reversed; the convictions on counts two and three are vacated. The matter is remanded for dismissal of count one and for further proceedings not inconsistent with the foregoing in connection with counts two and three.