WILKINSON, Circuit Judge:
Defendants appeal from their convictions for evasion of federal income taxes. We find that their contested business practices raise novel questions of tax liability to which governing law offers no clear guidance. Because the defendants therefore could not have ascertained the legal standards applicable to their conduct, criminal proceedings may not be used to define and punish an alleged failure to conform to those standards. We reverse the convictions.
I
James G. Mallas and Robert V. Jones, Jr., investment counselors in Charlotte, North Carolina, began in 1977 to design a tax shelter program based on deductions allowed to participants in coal-mining enterprises. Mallas, as sole shareholder, formed Genesis Leases, Inc., for the corporate purpose of locating and purchasing leases of coal property in Kentucky. Jones, as sole shareholder, formed Trinity Properties, Inc., which would sublease the coal rights from Genesis for $3.40 per extracted ton. Trinity would then re-sublease its rights to individual investors for $3.50 per extracted ton. These investors would contract to pay Trinity an advance minimum royalty during each year for the four-year lease period. In return, Trinity warranted that economically recoverable coal in the leased property was sufficient to permit the investor to recoup his advance minimum royalties; if the coal reserves proved to be inadequate, Trinity promised to supplement the lease with other property that would allow for complete recoupment. Finally, Mallas, as sole shareholder, formed Omega Energy, Inc., to purchase from the individual investors, for specified royalties, their rights to mine coal. Omega would then mine and market the coal, either by itself or by subcontract.
Omega Energy also served an important purpose in the financial structure of Mallas and Jones’s tax shelter program. The investor, who was obligated to pay Trinity an individually negotiated advance minimum royalty, had to pay at least 2/7 of that amount from personal funds. The investor could then, if he wished, borrow the remaining 5/7 from Omega in exchange for a non-recourse promissory note secured by the investor’s subleased mineral rights. As Omega mined and sold each ton of coal, it would retire the non-recourse note by retaining half of the royalty that it owed the investor. Omega financed these loans by borrowing Trinity funds that had been accumulated from the investors’ initial personal payments. Through such loans by Trinity to Omega and by Omega to the investors, Omega was able to fund 5/7 of every electing investor’s obligation to Trinity without an outside source of funding.
According to its promoters, the MallasJones program offered significant tax savings to prospective investors. Under Treasury Regulation § 1.612-3(b)(3), the advance minimum royalty was deductible at the taxpayer’s option either when the royalty was paid or when the coal was mined and sold. For a deduction taken at payment, an investor who had received an Omega loan for 5/7 of the royalty obligation would receive $3.50 of deduction for every $1.00 invested. This opportunity attracted fifty-three investors to the leasing venture in 1977, and Mallas and Jones created a parallel 1978 program with eighty-nine investors.
According to the government, however, the annual minimum royalties were not deductible and the entire shelter was an illegal scheme to evade federal income taxes. The government raised two specific objections to the program. First, it maintained that Treasury Regulation § 1.612-3(b)(3) authorized deductions only if Trinity, at the beginning of each lease, committed to that leasing investor enough coal property to recoup all of the annual advance minimum royalties due over the full four years of the lease. Trinity, which did not own that much coal, asserted to the contrary that the regulation required it to have sufficient coal to permit recoupment of the minimum royalty payments only at the time that each obligation became due. Under this interpretation, Trinity’s holdings were satisfactory. Second, the government reasoned that the advance minimum royalties were not deductible because — upon close analysis of the loan network connecting Trinity, Omega, and the investors — the royalties had not been paid in “cash or its equivalent” as required by Helvering v. Price, 309 U.S. 409, 413, 60 S.Ct. 673, 675, 84 L.Ed. 836 (1940), and constituted an economic transaction in form but not in substance.
With these alternative government theories cast into criminal charges, a grand jury in the western district of North Carolina indicted Mallas and Jones on thirty-five counts for violations related to the alleged tax evasion. The two men stood trial in January 1984 and were each convicted on fourteen counts: one count of conspiracy to defraud the United States by defeating the lawful functions of the Internal Revenue Service, 18 U.S.C. § 371; two counts of willfully claiming false deductions on their 1977 and 1978 tax returns for their own participation in the coal-leasing programs, 26 U.S.C. § 7206(1); ten counts of aiding others in the filing of false returns based on those persons’ investments in the program, 26 U.S.C. § 7206(2); and one count of causing a person to travel interstate ■ in furtherance of a scheme to defraud, 18 U.S.C. § 2314. The court imposed prison sentences of twelve years on each defendant, fined Mallas $75,000 and Jones $40,000, and ordered them to pay the costs of prosecution and all taxes owed to the United States. This appeal followed.
II
We reverse. Grave penalties rest in this case on an unsubstantiated theory of tax law: that the defendants promoted fraudulent deductions if the Trinity coal holdings were not sufficient to warrant complete recoupment of all advance royalties at the beginning of the lease but were sufficient to warrant complete recoupment of all advanee royalties as each annual payment fell due. Whatever eventual success this proposition may enjoy as an interpretation of tax law — a destiny we do not influence here — present authority in support of the theory is far too tenuous and competing interpretations of the applicable law far too reasonable to justify these convictions.
“It is settled,” this court observed in the analagous criminal tax case of United States v. Critzer, “that where the law is vague or highly debatable, a defendant— actually or imputedly — lacks the requisite intent to violate it.” 498 F.2d 1160, 1162 (4th Cir.1974). Criminal prosecution for the violation of an unclear duty itself violates the clear constitutional duty of the government to warn citizens whether particular conduct is legal or illegal. See generally Note, Criminal Liability for Evasion of an Uncertain Tax, 81 Col.L.Rev. 1348 (1981). As Critzer indicates, this same requirement arises from the rule of 26 U.S.C. § 7206 that only a “willful” tax evasion is criminal. Willful conduct under § 7206, which the Supreme Court described in United States v. Pomponio as “voluntary intentional violation of a known duty,” 429 U.S. 10, 12, 97 S.Ct. 22, 23, 50 L.Ed.2d 12 (1976), requires that the duty involved must be knowable. See also James v. United States, 366 U.S. 213, 221-222, 81 S.Ct. 1052, 1056-1057, 6 L.Ed.2d 246 (1961).
Whether annual advance minimum royalties that are recoupable from warranted coal reserves acquired after execution of a lease but before payment of the royalty may be deducted from gross income is a point of law that is “vague or highly debatable” in the sense identified by United States v. Critzer, As the government concedes in its brief, the applicable Treasury regulation, § 1.612-3(b), “does not explicitly state that an AMRP is deductible in the year paid only if there are sufficient reserves committed in the first year of a lease such that the total amount of all the AMRP’s required under the lease can be recouped.” The regulation, which merely indicates that the royalties are to be “paid or accrued in connection with mineral property as a result of a minimum royalty provision,” does not address the issue. In the absence of explicit language in the regulation, potential liability might alternatively be announced by “authoritative constructions sufficiently illuminating the contours of an otherwise vague prohibition,” Dombrowski v. Pfister, 380 U.S. 479, 490-91, 85 S.Ct. 1116, 14 L.Ed.2d 22 (1965). But the government has failed to suggest any other regulation, judicial decision, or even revenue ruling that sheds such light on this aspect of § 1.612-3(b). Nor have we found any. The traditional sources of notice for potential defendants are simply silent — and hence ambiguous — on this subject.
We recognize that due process does not require the prosecution to cite a “litigated fact pattern directly on point,” United States v. Ingredient Technology Corp., 698 F.2d 88, 96 (2d Cir.1983), cert. denied, 462 U.S. 1131, 103 S.Ct. 3111, 77 L.Ed.2d 1366 (1983), quoting United States v. Brown, 555 F.2d 336, 339-340 (2d Cir.1977). We are accordingly open to the government’s suggestion that a duty not articulated by regulatory language or judicial construction may nonetheless be compelled by the authoritative force of common sense. But the prosecution and the defense can in this situation both offer plausible support for their positions. As the government argues, using the date of lease execution as the crucial moment for defendants’ reserves serves the policy of § 1.612-3(b) that coal leasing arrangements be a single, simple transaction, a goal otherwise expressed in the requirements that advance royalties be uniform, that they be due for every year, and that the taxpayer elect in the first year whether to deduct all royalties at the time of payment or at the time of the mineral sale. Contrary to the conclusion of the government, however, a determination that the prosecution theory of § 1.612-3(b) is “reasonable and well-supported” does not prove that “defendants’ claim that they could not have known what the law required is frivolous.” Defendants, too, advance a “reasonable and well-supported” reading of § 1.612-3(b). As they point out, using the date of payment as the crucial moment for defendants’ reserves permits greater sensitivity to the fluctuating coal market and follows the rule that the tax status of payments made under a long-term agreement is determined by conditions existing at the time of the deductible payment.
Nothing here is meant to imply that one of these solutions is not a better construction of tax law, or that civil liability — with appropriate civil penalties — may not be imposed on these defendants for deductions claimed without a foundation in sufficient coal reserves. Compare United States v. Dahlstrom, 713 F.2d 1423 (9th Cir.1983), cert. denied, — U.S.-, 104 S.Ct. 2363, 80 L.Ed.2d 835 (1984) with Zmuda v. Commissioner of Internal Revenue, 731 F.2d 1417 (9th Cir.1984) (criminal conviction vacated but civil liability imposed in connection with same tax shelter). We merely find that there has been no “fair warning ... given to the world in language that the common world will understand, of what the law intends to do if a certain line is passed.” McBoyle v. United States, 283 U.S. 25, 27, 51 S.Ct. 340, 341, 75 L.Ed. 816 (1931) (Holmes, J.). The government may face a difficult task in translating the deductibility of annual advance minimum royalty payments into language that the common world will understand. But without that fair warning, the government may not institute criminal proceedings. As this court noted in United States v. Critzer, “the appropriate vehicle to decide this pioneering interpretation of tax liability is the civil procedure of administrative assessment,” not a criminal prosecution. 498 F.2d at 1164. We therefore reverse these judgments of conviction and remand the case for proceedings consistent with this opinion.
REVERSED.
. The investors did not personally participate in handling these loans. Each investor authorized Jones to negotiate through Trinity checks payable to the investor that were delivered to Jones by Omega. Trinity therefore wrote and delivered checks to Omega, which wrote checks to investors and delivered them to Trinity.
. Here, as throughout this opinion, we view the facts in the light most favorable to the government. Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942). Defendants argued at trial that their coal holdings were adequate under the government’s theory.
. Because the jury considered alternate theories of liability, we must reverse the convictions if either theory is an improper basis for punishment. Chiarella v. United States, 445 U.S. 222, 237 n. 21, 100 S.Ct. 1108, 1119 n. 21, 63 L.Ed.2d 348 (1980); Leary v. United States, 395 U.S. 6, 31-32, 89 S.Ct. 1532, 1545-1546, 23 L.Ed.2d 57 (1969). We cannot conclude "with a high degree of probability" that the jury here did not rely on the unsupported theory of inadequate coal reserves. Cf. United States v. Alexander, 748 F.2d 185, 189 (4th Cir.1985). We therefore need not address appellants’ additional claim that the royalties were paid in “cash or its equivalent” in a substantial economic transaction or their claim that the jury charge failed to explain the “form versus substance” doctrine of Bridges v. Commissioner of Internal Revenue, 325 F.2d 180 (4th Cir.1963) with sufficient precision to sustain these convictions.
. The uncertainty of a tax law, like all questions of vagueness, is decided by the court as an issue of law. Critzer, 498 F.2d at 1162. To the extent that the Fifth Circuit has adopted a contrary approach in United States v. Garber, 607 F.2d 92 (5th Cir.1979) (en banc), we decline to follow that rule. See United States v. Ingredient Technology Corp., 698 F.2d 88, 96-97 (2d Cir.1983), cert. denied, 462 U.S. 1131, 103 S.Ct. 3111, 77 L.Ed.2d 1366 (1983).
. To the contrary, we note that the Ninth Circuit has described the coal reserve requirements of § 1.612-3(b) as unsettled during this period. Redhouse v. Commissioner of Internal Revenue, 728 F.2d 1249, 1252 (9th Cir.1984), citing Pomerance, Coal-Leasing Arrangements Offer Substantial Tax Shelter Benefits, 44 J. Tax’n 350 (1976).