Defendants Angela Starks and Andrew Siegel seek to overturn their convictions under the anti-kickback provision of the Social Security Act, 42 U.S.C. § 1320a-7b (“the Anti-Kickback statute”). Specifically, Starks and Siegel argue that the district court erred by refusing to instruct the jury concerning the relevant mens rea. In addition, Starks and Siegel contend that the Anti-Kickback statute is unconstitutionally vague. While denying the defendants’ allegations of error, the government cross-appeals Siegel’s sentence on the grounds that the district court should not have reduced his offense level for acceptance of responsibility, and that the district court should have applied the guideline for bribery of a public official rather than the guideline for fraud and deceit. We AFFIRM IN PART, REVERSE IN PART, and REMAND.

BACKGROUND ^[1]

In 1992, Andrew Siegel was both the president and the sole shareholder of Future Steps, Inc., a corporation that developed and operated treatment programs for drug addiction. On April 22, 1992, Future Steps contracted with Florida CHS, Inc. to run a chemical dependency unit for pregnant women at Florida CHS’s Metropolitan General Hospital (“the Hospital”). In return, Florida CHS promised to pay Future Steps a share of the- Hospital’s profits from the program. As a Medicaid provider, the Hospital performed medical services for indigent and disabled persons and received payment for these activities through Consultec, the fiscal intermediary for the Florida Medicaid program. Before executing the Future Steps-Florida CHS contract, Siegel initialed each page of the agreement, which included a provision explicitly forbidding Future Steps from making any payment for patient referrals in violation of the Anti-Kickback statute.

At the time Siegel signed this contract, Angela Starks and Barbara Henry had just become community health aides in the employ of the State of Florida Department of[*836] Health and Rehabilitative Services (“HRS”). ^[2] Although Starks and Henry were employees of HRS, they actually worked in a federally-funded research project in Tampa, Florida known as “Project Support.” As part of their duties, Starks and Henry advised pregnant women about possible treatment for drug abuse. Upon beginning their work at HRS, Starks and Henry learned from their supervisor both that they could not accept any outside employment that might pose a conflict of interest with their work at HRS and that they were obligated to report any outside employment to HRS.

During the spring of 1992, Future Steps had difficulty attracting patients. One of Future Steps’s salaried “liaison workers,” Robin Doud-Lacher, however, identified Project Support as a potential source of referrals because of its relationship with high-risk pregnant women. When Doud-Lacher’s initial efforts to establish a referral relationship between Future Steps and Project Support failed, Siegel suggested to Doud-Lacher that she spend more time at Project Support, give diapers to Project Support, take Project Support workers to lunch, and otherwise build a relationship with Project Support’s employees.

During one of her subsequent visits to Project Support, Doud-Lacher learned from Starks and Henry that cuts in federal spending threatened to reduce their work hours. When Starks and Henry asked if Doud-Loucher knew of other available work, she promised to inquire for them about opportunities at Future Steps.

After discussing Starks and Henry’s interest with her immediate supervisor, Doud-Lacher spoke directly with Siegel about hiring the two women. Despite Starks and Henry’s extant employment with HRS, Sie-gel told Doud-Loucher that he would pay Starks and Henry $250 for each patient they referred: $125 when a referred woman began inpatient drug treatment with Future Steps and $125 after each such woman had stayed in Future Steps’s program for two weeks. ^[3] After accepting Siegel’s terms, Starks and Henry did not report their referral arrangement to anyone at Project Support or HRS.

At the outset of their work for Future Steps, Starks and Henry received checks written on Future Steps’s account and signed by Siegel. Before issuing these checks, Sie-gel verified that the referred patients had actually entered the Future Steps program; he did not, though, verify that the referrals were legal. Although the checks Siegel signed were coded variously as payments for aftercare, counseling, and marketing expenses, Siegel was actually only paying Starks and Henry for their referrals. In fact, Siegel did not at any time pay Starks and Henry for any of their time, effort, or business expenses, or for any covered Medicare service.

When Doud-Lacher left Future Steps, Sie-gel had Michael lx, another liaison worker, assume responsibility for the Starks and Henry referral arrangement. Generally, either Starks or Henry would call lx and ask him to pick up a referral directly from the Project Support clinic. When lx arrived at Future Steps with the referred patient, Sie-gel would give lx a check for Starks and Henry. Later, after Henry told lx that she did not want anyone at Project Support to see her receiving checks from Future Steps, lx agreed to deliver the checks to Starks and Henry either in the Project Support parking lot or at a restaurant. Between June 1992 and January 1993, Future Steps wrote checks payable to Starks totaling $2750 and to Henry totaling $1975.

At the end of 1992, Future Steps began paying Starks and Henry in cash. To make these payments, lx would withdraw cash from his personal bank account and meet Starks and Henry either at a restaurant or at a twelve-step program; Siegel and Future[*837] Steps would then reimburse lx. On one occasion, Siegel accomplished this reimbursement by meeting lx in a restaurant restroom and giving him $600. In total, lx paid Starks and Henry approximately $1000 to $1200 in cash.

Beyond the impropriety of Starks and Henry’s acceptance of referral payments from Siegel, the referral arrangement directly affected Starks and Henry’s counseling of the pregnant women who relied on them and Project Support for help. At trial, several of Future Steps’s clients testified that Starks and Henry threatened that HRS would take away their babies if they did not receive treatment for their drug addictions; in some instances, Starks and Henry threatened women with the loss of their babies if they did not go specifically to Future Steps. According to these women’s testimony, Starks and Henry informed them only about Future Steps’s program (eschewing discussion of alternative treatments), and most waited with Starks and Henry at the Project Support clinic until someone from Future Steps arrived to take them to the Hospital. Starks and Henry’s physician supervisor also testified that she told the two HRS employees to be more evenhanded in their advice to Project Support’s patients, after the number of women going to Future Steps from Project Support increased substantially.

In total, Starks and Henry referred eighteen women from Project Support to Future Steps. From these referrals, the Hospital received $823,023.04 in Medicaid payments.

On July 29, 1994, a federal grand jury indicted Siegel, Starks, Henry, and Doud-Lacher on five counts related to the referrals. Count One charged all four defendants with conspiring against the United States, in violation of 18 U.S.C. § 371, by offering to pay remuneration for referral of Medicare patients, in violation of 42 U.S.C. § 1320a-7b(b)(2)(A), and by soliciting and receiving such referral payments, in violation of 42 U.S.C. § 1320a-7b(b)(1)(A). Counts Two and Three charged Siegel and Doud-Loucher with paying remuneration to Starks and Henry to induce referrals of Medicaid patients, in violation of 42 U.S.C. § 1320a-7b(b)(2)(A). Finally, Count Four charged Starks and Count Five charged Henry with soliciting and receiving referral payments, in violation of 42 U.S.C. § 1320a-7b(b)(l)(A).

On February 22, 1996, the jury returned guilty verdicts as to all of the defendants on all five counts. Thereafter, the district court sentenced Siegel to serve three concurrent terms of twenty-four months of imprisonment and five years supervised release. In choosing this sentence, the district court reduced Siegel’s offense level under U.S.S.G. § 3E1.1 for acceptance of responsibility and applied the guideline for fraud, U.S.S.G. § 2F1.1. The district court sentenced Starks to two concurrent terms of thirty months of home detention.

DISCUSSION

On appeal, defendants Starks and- Siegel renew two contentions from their trial. First, they claim that the district court committed reversible error when it refused to instruct the jury that, , because of the Anti-Kickback statute’s mens rea requirement, Starks and Siegel had to have known that their referral arrangement violated the Anti-Kickback statute in order to be convicted. Second, Starks and Siegel argue that the Social Security Act’s prohibition on paid referrals, when considered together with the Act’s safe harbor provision, 42 U.S.C. § 1320a-7b(b)(3) (“the Safe Harbor provision”), is unconstitutionally vague. We address each of these arguments before turning to the government’s cross-appeals concerning Siegel’s sentence.

I. STARKS AND SIEGEL’S APPEALS

A. THE “WILLFULLY” INSTRUCTION

Starks and Siegel "argue that the district court erred in its instruction concerning the mens rea required under the Anti-Kickback statute. ’ According to 42 U.S.C. § 1320a-7b(b), it is illegal for a person to “knowingly and willfully solicit[ ] or receive[ ] any remuneration” for referrals for services covered by the federal government. At trial, the district court gave our circuit’s pattern instruction regarding the term “willfully”:

The word willfully, as that term is used from time to time in these instructions,[*838] means the act was committed voluntarily and purposely, with the specific intent to do something the law forbids, that is with a bad purpose, either to disobey or disregard the law.

R26 at 18; see also 11th Cir. Pattern Jury Instr. 9.1. In reviewing the district court’s charge, we determine whether the court’s instructions as a whole sufficiently informed the jurors so that they understood the issues and were not misled. See U.S. v. Hooshmand, 931 F.2d 725, 733 (11th Cir.1991). ^[4]

In support of their claim, Starks and Siegel rely heavily on United States v. Sanchez-Corcino, 85 F.3d 549 (11th Cir.1996), and Ratzlaf v. United States, 510 U.S. 135, 114 S.Ct. 655, 126 L.Ed.2d 615 (1994). Since we heard oral argument on this ease, however, the Supreme Court has issued an opinion in Bryan v. United States, — U.S. -, 118 S.Ct. 1939, 141 L.Ed.2d 197 (1998), that clearly refutes Starks and Siegel’s position.

In Sanchez-Corcino, a panel of this court held that the term “willfully” in 18 U.S.C. § 922(a)(1)(D) (requiring license for firearms), meant that the government had to prove that a defendant “acted with knowledge of the [§ 922(a)(1)(D)] licensing requirement.” Id. at 553, 554 (“[k]nowledge of the general illegality of one’s conduct is not the same as knowledge that one is violating a specific rule”). In Bryan, though, the Supreme Court explicitly rejected our decision in Sanchez-Corcino. See Bryan, — U.S. at -, 118 S.Ct. at 1946. According to the Bryan Court, a jury may find a defendant guilty of violating a statute employing the word “willfully” if it believes “that the defendant acted with an evil-meaning mind, that is to say, that he acted with knowledge that his conduct was unlawful.” Id. at -, 118 S.Ct. at 1946. Further, the Supreme Court distinguished tax or financial eases, such as Rat-zlaf, that “involved highly technical statutes that presented the danger of ensnaring individuals engaged in apparently innocent conduct.” Id. ^[5] Because “the jury found that [the defendant] knew that his conduct was unlawful,” the Bryan Court wrote, “[t]he danger of convicting individuals engaged in apparently innocent activity that motivated our decisions in the tax cases and Ratzlaf is not present here.” Id. (footnote omitted). Thus, the Court held that “the willfulness requirement of § 924(a)(1)(D) does not carve out an exemption to the traditional rule that ignorance of the law is no excuse; knowledge that conduct is unlawful is all that is required.” Id. 6

Analogously, the Anti-Kickback statute does not constitute a special exception. Section 1320a-7b is not a highly technical tax or financial regulation that poses a danger of ensnaring persons engaged in apparently innocent conduct. Indeed, the giving or taking of kickbacks for medical referrals is hardly the sort of activity a person might expect to be legal; compared to the licensing provisions that the Bryan Court considered, such kickbacks are more clearly malum in se, rather than malum prohibitum. Compare Bryan, — U.S. at -, 118 S.Ct. at 1946. ^[7][*839] Thus, we see no error in the district court’s refusal to give Starks and Siegel’s requested instruction. ^[8] Accord United States v. Davis, 132 F.3d 1092, 1094 (5th Cir.1998); United States v. Jain, 93 F.3d 436, 440 (8th Cir.1996), ce rt. denied, — U.S. -, 117 S.Ct. 2452, 138 L.Ed.2d 210 (1997); United States v. Bay State Ambulance and Hosp. Rental Serv., Inc., 874 F.2d 20, 33 (1st Cir.1989). But cf. Hanlester Network v. Shalala, 51 F.3d 1390, 1400 (9th Cir.1995).

B. VAGUENESS

Starks and Siegel also argue that the Anti-Kickback statute is unconstitutionally vague because people of ordinary intelligence in either of their positions could not have ascertained from a reading of its Safe Harbor provision that their conduct was illegal. ^[9] Under the Safe Harbor provision, the Anti-Kickback statute’s prohibition on referral payments

shall not apply to ... any amount paid by an employer to an employee (who has a bona fide employment relationship with such employer) for employment in the provision of covered items and services-

42 U.S.C. § 1320a-7b(b)(3); see also 42 C.F.R. § 1001.952. According to Starks and Siegel, this provision is vague because ordinary people in their position might reasonably have thought that Starks and Henry were “bona fide employees” who were exempt from the Anti-Kickback statute’s prohibition on remuneration for referrals.

Starks and Siegel are correct that a criminal statute must define an offense with sufficient clarity to enable ordinary people to understand what conduct is prohibited. See, e.g., Hofstatter, 8 F.3d at 321. Both the particular facts of this ease and the nature of the Anti-Kickback statute, however, undercut Starks and Siegel’s vagueness argument. First, even if Starks and Siegel believed that they were bona fide employees, they were not providing “covered items or services.” As the government has shown, Starks received payment from Siegel and Future Steps only for referrals and not for any legitimate service for which the Hospital received any Medicare reimbursement. At the same time, persons in either Siegel’s or Starks’s position could hardly have thought that either Starks or Henry was a bona fide employee; unlike all of Future Steps’s other workers, Starks and Henry did not receive regular salary checks at the Hospital. Instead, they clandestinely received their checks (often bearing false category codes) or cash in parking lots and other places outside the Project Support clinic so as to avoid detection by other Project Support workers.

Furthermore, beyond these particular facts, we see no reason to view the Anti-Kickback statute .as vague. In Village of Hoffman Estates v. The Flipside, 455 U.S. 489, 498-499, 102 S.Ct. 1186, 1193, 71 L.Ed.2d 362 (1982), the Supreme Court set out several factors for a court to consider in determining whether a statute is impermissi-bly vague, including whether the statute (1) involves only economic regulation, (2) provides only civil, rather than criminal, penalties, (3) contains a scienter requirement mitigating vagueness, and (4) threatens any constitutionally protected rights. As two of.[*840] our sister circuits have already concluded, these factors militate against finding the Anti-Kickback statute unconstitutional. See Hanlester, 51 F.3d at 1398; Bay State, 874 F.2d at 32-33. Indeed, the statute regulates only economic conduct, ^[10] and it does not chill any constitutional rights. Moreover, although the statute does provide for criminal penalties, it requires “knowing and willful” conduct, a mens tea standard that mitigates any otherwise inherent vagueness in the Anti-Kickback statutes’s provisions. Hanlester, 51 F.3d at 1398; Bay State, 874 F.2d at 33. In sum, we agree with the district court that the Anti-Kickback statute gave Starks and Siegel fair warning that their conduct was illegal and that the statute therefore is not unconstitutionally vague.

II. THE GOVERNMENT’S CROSS-APPEAL

In its cross-appeal, the government contends that the district court incorrectly granted Siegel a U.S.S.G. § 3E1.1 reduction for acceptance of responsibility. In addition, the government maintains that the district court erred by sentencing Siegel under the fraud and deceit guideline, U.S.S.G. § 2F1.1, rather than the bribery of a public official guideline, U.S.S.G. § 2C1.1.

A ACCEPTANCE OF RESPONSIBILITY

On appeal, the government argues that Siegel should not have received a three-level reduction for acceptance of responsibility because he denied having had any guilty intent. In response, Siegel contends that he was entitled to the reduction because he admitted all the relevant facts and cooperated with the government’s investigation, while preserving his legitimate legal position regarding the applicability of the statute to his conduct. We review the district court’s determination that Siegel accepted responsibility for clear error. United States v. Anderson, 23 F.3d 368, 369 (11th Cir.1994) (per curiam).

To receive a reduction under § 3E1.1, a defendant must prove that he clearly accepted responsibility for his offense. See id. The reduction does not apply to “a defendant who puts the government to its burden of proof at trial by denying the essential factual elements of guilt, is convicted, and only then admits guilt and expresses remorse.” U.S.S.G. § 3E1.1, comment, (n.2). Nonetheless, a defendant may, “[i]n rare situations,” be entitled to this reduction if he goes to trial to assert and preserve issues unrelated to factual guilt, such as the applicability of a statute to his conduct. Id. Still, a defendant who contends that he did not possess fraudulent intent is making a factual, not a legal, challenge to the government’s criminal allegations that precludes a sentence reduction for acceptance of responsibility. See United States v. Smith, 127 F.3d 987, 989 (11th Cir.1997) (en banc) cert. denied, — U.S. -, 118 S.Ct. 1202, 140 L.Ed.2d 330 (1998); see also Sanchez-Corcino, 85 F.3d at 555-56.

By its terms, 42 U.S.C. § 1320a-7b(b)(2) makes it illegal for any person knowingly to offer any payment “to induce” a referral for services covered by the federal government. Citing this provision, Siegel argues that by conceding at trial that he made payments to Starks and Henry, he admitted all the conduct prohibited by the statute. As the government correctly points out, however, Siegel has denied having had any intent to induce referrals, an essential element of the charges on which he was convicted. Because Siegel put the government to its burden of proof by contesting his intent to violate 42 U.S.C. § 1320a-7b(b), Siegel’s arguments at trial amounted to a factual denial of guilt and were therefore inconsistent with acceptance of responsibility. ^[11] Given the factual positions that Siegel[*841] has taken — and continues to take — we conclude that he should not have been eligible for a reduction for acceptance of responsibility and that the district court therefore clearly erred in awarding him a three-level reduction under § 3E1.1.

B. THE FRAUD AND DECEIT GUIDELINE

Additionally, the government argues that the court erred by sentencing Siegel under the § 2F1.1 “Fraud and Deceit” guideline rather than the § 2C1.1 “Bribe” of a public official guideline. Appendix A of the Sentencing Guidelines references three guideline sections which are applicable to violations of § 1320a-7b: U.S.S.G. § 2B1.1 (larceny), U.S.S.G. § 2B4.1 (commercial bribery), and § 2F1.1 (fraud). U.S.S.G. app. A, at 384. If more than one guideline section is referenced for the particular statute, Appendix A instructs the sentencing court to use the guideline most appropriate for the nature of the conduct charged. See U.S.S.G. app. A, at 373 (introduction). Further, the Appendix provides that if, “in an atypical case, the guideline section indicated for the statute of conviction is inappropriate because of the particular conduct involved, [courts should] use the guideline section most applicable to the nature of the offense conduct charged in the count of which the defendant was convicted.” Id. We review the district court’s determination of the applicable guideline de novo. United States v. Acanda, 19 F.3d 616, 618 (11th Cir.1994). ^[12]

Regarding the three guidelines listed as potentially applicable in Appendix A, the government and Siegel properly agree that Sie-gel should not be sentenced under § 2B1.1 or § 2B4.1. Since § 2B1.1 applies to crimes involving stolen property, it clearly has no relevance. Moreover, since § 2B4.1 applies only to “bribery offenses and kickbacks that do not involve officials of federal, state, or local government,” § 2B4.1 comment, (n.l), this guideline provision, too, cannot be appropriate for Siegel, who illegally induced referrals from a state employee working in a federal Medicare project. ^[13]

Siegel, however, asserts that the third listed guideline, § 2F1.1, is relevant and applicable. To support this position, which was also that of the district court, Siegel relies on United States v. Adam, 70 F.3d 776, 781 (4th Cir.1995). In that case, the Fourth Circuit affirmed a district court’s sentence, under § 2F1.1, of a physician who had violated the Anti-Kickback statute. Although Adam involved application of § 2F1.1 to the Anti-Kickback statute, we find the case to be of little help to our consideration of Siegel’s sentence, because the Adam court addressed only the district court’s calculation of the government’s “loss,” without discussing whether § 2F1.1 or some other provision was the most appropriate guideline. See id. at 781-82.

Further, we see little reason to view § 2F1.1 as any more applicable to Siegel’s conduct than § 2B1.1 or § 2B4.1. As a central part of any application of § 2F1.1, a district court must calculate the “loss” suffered by the defrauded or deceived victim. See generally § 2F1.1. Yet, in this case Sie-gel did not steal from anyone, including the government; Siegel did not file false Medicare claims but rather engaged in a kickback scheme that corrupted Project Support’s referral process. While a district court should sentence persons committing Anti-Kickback crimes involving fraud or false statements[*842] raider § 2F1.1, this provision is not appropriate for this case.

In fact, Siegel’s crime presents the “atypical case” in which the listed guideline for the Anti-Kickback statute is inapposite and a court should resort to a more applicable section, in this instance § 2C1.1. First, we note that the term “induce” in 42 U.S.C. § 1320a-7b(b)(2) can be reasonably understood in this case to connote bribery. Indeed, the term “induce” is defined as “[t]o bring on or about, to affect, cause, to influence to an act or course of conduct ...,” Black’s Law Dictionary at 775; in the context of this case, “induce” and “bribe” are thus virtually synonymous, since Siegel induced Starks and Henry to refer patients to Future Steps through illicit payments. Compare id. at 191 (“Any money, ... preferment ... or undertaking to give any [money or preferment] ... with a corrupt intent to induce ... action, vote, or opinion _ ”) (emphasis added). See also United States v. Kummer, 89 F.3d 1536, 1540 (11th Cir.1996) (discussing meaning of “bribe”). Second, the Anti-Kickback statute explicitly refers to “kickbacks, bribes, and rebates” as prohibited forms of remuneration for referrals, bringing Siegel’s crime within the purview of the terms of § 2C1.1. See 42 U.S.C. § 1320a-7b(b)(2)(A). Thus, the indictment and jury instructions in this ease referred to payment of “remuneration (including kickbacks, bribes, or rebates).” Rl-2 at 3 (indictment); see also R26 at 24 (instruction defining remuneration). Finally, by paying Starks and Henry for referrals, Siegel sought to corrupt their execution of their duties as state employees and workers in a federal program — just the sort of corrosive activity that the Sentencing Commission designed § 2C1.1 to punish. Cf. § 2C1.1 comment, (background). ^[14] Therefore, we hold that the district court erred in applying § 2F1.1 rather than § 2C1.1 in sentencing Siegel.

CONCLUSION

In this case, Starks and Siegel ask that we reverse their convictions for violating and conspiring to violate the Anti-Kickback statute, while the government requests that we reverse the district court’s application of two guideline provisions to Siegel’s sentence. With regard to Starks and Siegel’s appeal, we hold that the district court did not err when it refused to give their requested instruction, and that the Anti-Kickback statute is not unconstitutionally vague as applied to Starks and Siegel. Therefore, we AFFIRM these parts of the district court’s judgment. With regard to the government’s cross-appeal, we hold that the district court clearly erred in granting Siegel a reduction for acceptance of responsibility, and we conclude that the district court should have sentenced Siegel under § 2C1.1 rather than § 2F1.1. Therefore, we REVERSE these parts of the district court’s judgment and REMAND for further proceedings consistent with this opinion.

AFFIRMED IN PART, REVERSED IÑ PART, and REMANDED.