CUMMINGS, Circuit Judge.
Dennis G. Antzoulatos, a used car dealer in Milwaukee, pled guilty to one count of conspiring to launder money in violation of 18 U.S.C. § 1956(a)(1)(B) and was sentenced to 52 months in prison. He now appeals, claiming that the statute as applied to him violates his due process rights under the Constitution. The plea agreement Antzou-latos signed preserves his right to appeal this issue. Antzoulatos also appeals his sentence, arguing that the district court erred in not giving him credit for acceptance of responsibility under the Guidelines.
I.
Antzoulatos owned and operated a used car dealership in Milwaukee, Wisconsin, under the name of D & S Auto Sales (“D & S”) between December 1985 and February 1989, and under the name of Olympic Auto Sales between February 1989 and September 1990. During this time period, Antzou-latos sold cars to Billy Cannon, James Ver-ser, Greg Farrow, Errol Jackson and Hays Barker, all of whom Antzoulatos admits were involved in selling cocaine during that time. Antzoulatos titled the cars in names other than those of the above drug dealers — on several occasions the cars were titled in the name of D & S. Antzoulatos denies that he knew at the time he sold the cars that these men were drug dealers or that the mistitling was done for the purpose of hiding the proceeds of drug transactions.
A federal grand jury handed down a four-count indictment against Antzoulatos and his employee Grace Jim on September 11, 1990. Count one of the indictment charged Antzoulatos with being a member of a conspiracy whose object was to conduct financial transactions involving the proceeds of specified unlawful activity involving controlled substances in violation of 18 U.S.C. § 1956(a)(1)(B). The indictment alleged that the defendant or Grace Jim performed a number of overt acts in furtherance of the conspiracy, including selling numerous cars and trucks to drug dealers and titling them in other persons’ names between 1986 and 1990. One transaction with Errol Jackson is outlined in detail by the indictment. On January 28, 1987, Antzoulatos allegedly bought a 1985 Mercedes-Benz 380 SE from the Metro Milwaukee Auto Auction by check for $32,525 on behalf of Errol Jackson. On that day, Antzoulatos deposited $25,000 in cash in the checking account of D & S, and the following day made separate deposits of $6,500 and $1,000 to that account. This car was sold on August 2, 1988, to Billy Cannon. A state of Wisconsin application for title listed D & S as the seller when it was in fact purchased from Errol Jackson. On December 19, 1989, Antzoulatos advised Billy Cannon to lie to federal agents if questioned about the purchase of the 1985 Mercedes-Benz.
The Pre-Sentence Report presents in more detail Antzoulatos’ close relationship with Jackson and the other cocaine dealers. Greg Farrow purchased two cars from Ant-zoulatos, and told him that he did not want the cars titled in his name because he did not want them linked to him. The vehicles were therefore placed in the name of Farrow’s mother and girlfriend. James Verser purchased four cars from Antzoulatos, and also told him he did not want to be linked to the cars. The cars were titled in the name of others; one of Verser’s cars was titled in the name of his one-year-old nephew. Hays Barker purchased approximately 20 cars from Antzoulatos, many of which were titled in fictional names. According to the Pre-Sentence Report, Barker would use a particular car for two to three weeks for delivering drugs and then trade it in on the purchase of another vehicle.
Errol Jackson had a particularly close relationship with Antzoulatos. Antzoula-tos paid Jackson $500 a week in order to give Jackson the appearance of an employee, even though Jackson did not work at Antzoulatos’ dealership in any traditional sense of the term. Indeed, Jackson apparently repaid his “salary” to Antzoulatos under the table. Jackson did insist on retaining 50 percent of the profits from certain customers he was bringing into the car lot. Jackson also ensured that his personal cars were titled in the name of D & S. In addition to using the Mercedes referred to above, Jackson bought with a D & S buyer’s card a 1984 Rolls Royce Silver Spur valued at $57,900 at a Chicago Automobile Auction, forging Antzoulatos’ signature on a purchase agreement. Jackson paid for the Rolls Royce with seven different cashier’s checks purchased at different banks in order to avoid having any one bank generate a Currency Transaction Report. The Rolls Royce was also titled in the name of D & S, and like the Mercedes was used by Jackson as his personal car. Jackson in similar fashion also purchased a Chevrolet Blazer at an automobile auction, made sure it was placed in the name of D & S, and used it as his personal car.
The Pre-Sentence Report indicates that Farrow, Verser, Barker and Jackson all told Antzoulatos that they were drug dealers and that they needed to mistitle their cars in order to conceal the profits from their drug dealings. Antzoulatos denies this, admitting only that he had heard hearsay and rumors from other sources that these individuals were involved in drugs. Antzoulatos also vehemently denied allegations in the Report that he was personally involved in drug dealing. Antzoulatos did not deny any other facts outlined in the Report.
On the day before his trial was scheduled to begin, after his co-defendant Jim indicated that she would testify-against him, Antzoulatos decided to enter a plea agreement. The plea agreement states that “[t]he defendant acknowledges, understands and agrees * * * that defendant is, in fact, guilty of the offense [described in Count one of the indictment].” R. 52 at 7. Antzoulatos therefore agreed that he engaged in financial transactions knowing that the property involved represented the proceeds of unlawful activity, and knowing that the transactions were designed to conceal the nature or source of the proceeds or to avoid a transaction reporting requirement. At the plea hearing, Antzoulatos acknowledged his role in the transactions described above, but continued to maintain that he did not know at that time that these persons were drug dealers. Antzoulatos’ attorney prompted Antzoulatos at the hearing several times to admit only that “he should have known.” There is absolutely no indication that a jury would have been allowed to convict Antzoulatos on a simple negligence standard; indeed, the government proposed a jury instruction regarding the definition of “knowingly” that included a discussion of conscious avoidance and did not include the phrase “should have known.”
At the sentencing hearing, the colloquy concerning Antzoulatos’ state of mind continued. The judge did not make an explicit finding that Antzoulatos actually, subjectively knew that the persons he dealt with were drug dealers. Judge Curran’s statements at the sentencing hearing reveal, however, that he believed that Antzoulatos either knew or at the very least deliberately turned a blind eye towards the fact of his customers’ ill-gotten gains:
—[T]he Court finds almost impossible to imagine that [Antzoulatos] could not have been aware of [Jackson, Cannon, Farrow and Barker’s activities], R. 68 at 16.
—Now if there’s a group in our society who is more inquisitive about who you are and where you work and how much money you’ve got than a car salesman, I haven’t met that person. * * * [Antzou-latos’ story] is a little like the old story of the piano player and the whore house, claiming he doesn’t know what’s going on upstairs. Id. at 25.
—It doesn’t seem to me that you can simply sit like Pontious Pilot [sic] and say I didn’t see any evil and I didn’t do any evil * * *. Id. at 37.
II.
Antzoulatos challenges the constitutionality of 18 U.S.C. Section 1956(a)(1)(B) as applied to him. This provision of the Money Laundering Act of 1986 provides that:
(a)(1) Whoever, knowing that the property involved in a financial transaction represents the proceeds of some form of unlawful activity, conducts or attempts to conduct such a financial transaction which in fact involves the proceeds of specified unlawful activity—
(B) Knowing that the transaction is designed in whole or in part—
(i) to conceal or disguise the nature, the location, the source, the ownership, or the control of the proceeds of specified unlawful activity; or
(ii) to avoid a transaction reporting requirement under State or Federal Law,
shall be sentenced * * *.
To summarize, then, a conviction under this part of the statute requires the government to prove the following:
(1) that the defendant took part in a financial transaction involving the proceeds of specified unlawful activity;
(2) that the defendant knew that the property involved was the proceeds of specified unlawful activity; and
(3) that the defendant knew that the transaction was designed, in whole or in part, either to (a) conceal or disguise the proceeds, or (b) avoid a transaction reporting requirement.
Antzoulatos contends that when applied to a merchant like himself, the Money Laundering Act violates his substantive due process right to engage in a lawful occupation. Antzoulatos also contends that the Act as applied to him is void for vagueness.
We are unable to locate any reported case that has discussed the constitutionality of Section 1956(a)(1)(B) in relation to a money laundering financial transaction as applied to a seller who is not charged with the underlying criminal activity. The majority of reported eases involve a defendant charged with both drug dealing and money laundering — i.e., they involve drug dealers laundering their drug money. In these cases, the drug dealer is the “purchaser” in the money laundering financial transaction who uses his ill-gotten proceeds to buy various goods or services, or who otherwise tries to hide his proceeds. Nothing in the language of Section 1956(a)(1)(B), however, distinguishes between persons directly involved in the unlawful activity and those involved only in laundering the proceeds of the unlawful activity.
Throughout his constitutional arguments, Antzoulatos intimates that he is only guilty of negligence, that he “should have known” that the customers listed in the indictment were drug dealers. Significantly, however, Antzoulatos makes no claim on appeal that his guilty plea was involuntarily made under the belief that he could have been convicted under a simple negligence standard. He did not deny his involvement in any of the transactions outlined in the indictment and in the Pre-Sentence Report, but only denied any knowledge he was dealing with drug dealers. Antzoulatos declined the opportunity to go to trial and make the government prove that he knew the monies he received were proceeds from drug deals and also prove that he knew the purpose of the transactions was to disguise the nature or source of these funds. We agree with the trial judge that any lack of actual knowledge on Antzoulatos’ part amounted at a minimum to wilful blindness or conscious avoidance.
It is well settled that wilful blindness or conscious avoidance is the legal equivalent to knowledge. In the seminal case of United States v. Jewell, 532 F.2d 697 (9th Cir.1976), certiorari denied, 426 U.S. 951, 96 S.Ct. 3173, 49 L.Ed.2d 1188 the court upheld a jury instruction that a defendant “knowingly” possessed marijuana even if he was not actually aware it was in his car if “his ignorance in that regard was solely and entirely a result of his having made a conscious purpose to disregard the nature of that which was in the vehicle, with a conscious purpose to avoid learning the truth.” Id. at 700. This Court and other courts of appeals have consistently upheld the use of so-called ostrich instructions based on conscious avoidance when supported by the evidence. See United States v. Ramsey, 785 F.2d 184, 189-190 (7th Cir.1986) (collecting cases), certiorari denied, 476 U.S. 1186, 106 S.Ct. 2924, 91 L.Ed.2d 552; cf. United States v. Bader, 956 F.2d 708, 710 (7th Cir.1992) (construing the term knowingly in the Sentencing Guidelines to include more than “should have known” but noting the possibility of conscious avoidance).
We therefore examine the constitutionality of Section 1956(a)(1)(B) as applied to a merchant who actually knew that he was dealing with drug dealers and their money, or deliberately turned a blind eye regarding this fact. It should be stressed that we do not consider the constitutionality of a statute that imposes criminal penalties upon a merchant for selling goods to persons he “should have known” were laundering tainted money, or to persons he was merely suspicious were laundering tainted money.
Antzoulatos argues that his conviction violates his right to substantive due process as guaranteed by the Fifth Amendment. He posits either a liberty or property right to sell lawfully acquired goods to persons he does not actually know are drug dealers. The Supreme Court noted in 1923 that the concept of liberty in the due process clause
denotes not merely freedom from bodily restraint but also the right of the individual to contract, to engage in any of the common occupations of life, to acquire useful knowledge, to marry, establish a home and bring up children, to worship God * * *.
Meyer v. Nebraska, 262 U.S. 390, 399, 43 S.Ct. 625, 626, 67 L.Ed. 1042. The Supreme Court has on several occasions confirmed substantive due process rights for parents to educate their children outside of public schools (Wisconsin v. Yoder, 406 U.S. 205, 92 S.Ct. 1526, 32 L.Ed.2d 15; Pierce v. Society of Sisters, 268 U.S. 510, 45 S.Ct. 571, 69 L.Ed. 1070), for family members to live together (Moore v. City of East Cleveland, 431 U.S. 494, 97 S.Ct. 1932, 52 L.Ed.2d 531), and for women to choose abortions in certain circumstances (Roe v. Wade, 410 U.S. 113, 93 S.Ct. 705, 35 L.Ed.2d 147). Since the Lochher era, however, any substantive due process right to-contract, or to engage in a lawful occupation, has been sharply curtailed. See Moore, 431 U.S. at 501, 97 S.Ct. at 1936. As this Court has noted, “we do not consider [substantive due process] a blanket protection against unjustifiable interferences with property. That way Lochner lies.” Schroeder v. City of Chicago, 927 F.2d 957, 961 (1991).
Even if we were to accept that Antzoula-tos has a generalized liberty interest in selling lawfully acquired cars, we do not believe that the interest stretches so widely to immunize Antzoulatos’ conduct in this case. Section 1956(a)(1)(B) places but a narrow restriction on Antzoulatos’ ability to sell his merchandise. :He is only barred from selling, to persons he knows are drug dealers, and only then when the known purpose of the sale is to conceal the source, nature or ownership of the proceeds. Ant-zoulatos does not, and could not, assert that this restriction on his. right to sell his property amounts to a governmental taking. We conclude that Antzoulatos’ right to liberty under the Fifth Amendment was not violated.
Antzoulatos also argues that the Money Laundering Act is void-for-vagueness as applied to him. “The void-for-vagueness doctrine requires that a penal statute define the criminal offense with sufficient definiteness that ordinary people can understand what conduct is prohibited and in a manner that does not encourage arbitrary and discriminatory enforcement.” Kolender v. Lawson, 461 U.S. 352, 357, 103 S.Ct. 1855, 1858, 75 L.Ed.2d 903. The most important aspect of the doctrine is the requirement that the legislature establish minimal guidelines to govern the discretion of law enforcement officials. Id. at 358, 103 S.Ct. at 1858-59. Yet since legislatures are “condemned to the use of words, we can never expect mathematical certainty from our language.” Grayned v. City of Rockford, 408 U.S. 104, 110, 92 S.Ct. 2294, 2300, 33 L.Ed.2d 222.
Vagueness challenges to statutes which do not involve First Amendment freedoms must be examined in light of the facts of the case at hand. Chapman v. United States, — U.S. —, 111 S.Ct. 1919, 1929, 114 L.Ed.2d 524; Village of Hoffman Estates v. Flipside, Hoffman Estates, Inc., 455 U.S. 489, 495 n. 7, 102 S.Ct. 1186, 1191 n. 7, 71 L.Ed.2d 362. Regulation of economic activity, such as Antzoula-tos’ ability to sell cars, simply does not implicate the First Amendment. Cf. Village of Hoffman Estates v. Flipside, Hoffman Estates, Inc., 455 U.S. 489, 102 S.Ct. 1186 (drug paraphernalia law not vague as applied to shopkeeper); United States v. National Dairy Products Corp., 372 U.S. 29, 83 S.Ct. 594, 9 L.Ed.2d 561 (Robinson-Patman Act not vague as applied to businesses making sales below cost). Therefore, Antzoulatos’ vagueness arguments must be examined in light of the particular facts of his case.
We conclude that Section 1956 is not unconstitutionally vague as applied to Antzoulatos. This Court in United States v. Jackson, 935 F.2d 832 (1991), has already rejected a vagueness challenge to 18 U.S.C. Section 1956(a)(1). As we have done above, the Court in Jackson carefully examined the statute and noted that it requires the government to prove both that the defendant knew the proceeds involved in a particular transaction were of a specified unlawful activity, and that he knew the transaction was designed to conceal one of the enumerated attributes of these proceeds. Id. at 838-839.
These requirements of intent and knowledge “do[ ] much to destroy any force in the argument that application of the [statute] would be so unfair that it must be held invalid,” Boyce Motor Lines v. United States, 342 U.S. 337, 342 [72 S.Ct. 329, 332, 96 L.Ed. 367] * * *, “especially with regard to the adequacy of notice to the complainant that his conduct is proscribed.” Village of Hoffman Estates v. Flipside, Hoffman Estates, Inc., 455 U.S. 489, 499 [102 S.Ct. 1186, 1193, 71 L.Ed.2d 362] * * *.
Id. at 839. The Court also noted that the definitions included at 18 U.S.C. Sections 1956(c)(l)-(7) mitigate any possible vagueness of the terms used in the statute and show that Congress has adequately provided guidelines to law enforcement officials. Id. .
Antzoulatos correctly points out that the defendant in Jackson was convicted on separate counts of distributing drugs and laundering his own drug money by depositing it into a church bank account and using it to purchase various personal items. We agree that the vagueness question is closer here, where the statute is applied to a car dealer not directly involved in drug dealing. A drug dealer, if convicted on both a narcotics count and a money laundering count, by hypothesis knows that he is using tainted proceeds in the transaction, and also knows that his purpose is to conceal the nature or source of the proceeds. The merchant, on the other hand, has not been involved with the proceeds prior to the transaction.
The question therefore arises: how does the merchant “know” that a transaction is being consummated with tainted money and further know that the purpose is to conceal something about that money? It presumably would be sufficient when the merchant personally observes the unlawful activity and sees that the proceeds are being used to buy goods from him. It also is presumably sufficient if the buyer says directly to the merchant: “this money is tainted.” More problematic is asking the merchant to rely on the word of third persons, who may or may not be believable. Also problematic is permitting the merchant to rely on the appearance of a buyer, or on the presence of unexplained wealth.
We are confident that courts are capable of ferreting out prosecutions that present insufficient evidence of knowledge on the part of the merchant. The case of United States v. Campbell, 777 F.Supp. 1259 (W.D.N.C.1991), is a good example of a careful application of Section 1956(a)(1)(B) to a merchant. The defendant in Campbell was a real estate agent who facilitated the sale of a house to a drug dealer. The district court overturned the agent’s money-laundering conviction. Evidence that the buyer paid cash, the buyer was a “known” drug dealer in a town thirty miles away, the buyer dressed flashily, and the defendant’s associate told her that there “may have been drug money” involved was held insufficient to support a conclusion that the defendant knew that the buyer was paying for real estate with drug proceeds. Id. at 1268.
Focusing on the particular facts of this case, we conclude that Section 1956(a)(1)(B) is not unconstitutionally vague as applied. Unlike the defendant in Campbell, Antzou-latos is closely linked to the drug dealers with whom he dealt. Antzoulatos allowed one drug dealer access to his company’s cheeks to purchase cars at area auto auctions. He allowed this dealer on several occasions to pay him back in cash increments designed to avoid currency transaction requirements. Several of the customers were prepared to testify at trial that they told Antzoulatos directly that they were drug dealers and needed to conceal their drug profits. He mistitled scores of cars for his drug-dealing customers over a period of years. Antzoulatos decided to plead guilty and does not contend that this plea was involuntary or that a factual basis for his plea was not established. Given these circumstances, we believe that Ant-zoulatos was adequately put on notice that his conduct would be considered unlawful.
III.
Antzoulatos argues in the alternative that the trial court erred in denying him credit for acceptance of responsibility under U.S.S.G. § 3El.l(a). Under this section, a defendant is entitled to a 2-level offense level reduction “[i]f the defendant clearly demonstrates a recognition and affirmative acceptance of personal responsibility for his criminal conduct.” The district judge’s determination in this regard is a finding of fact that we may overturn only if it is clearly erroneous. United States v. Franklin, 902 F.2d 501, 505 (7th Cir.1990), certiorari denied, — U.S. — , 111 S.Ct. 274, 112 L.Ed.2d 229 Antzoulatos is not entitled to a reduction merely because he entered a guilty plea. U.S.S.G. § 3E1.1(c).
Because we are not left with the definite and firm conviction that a mistake has been committed, see Anderson v. City of Bessemer City, 470 U.S. 564, 573, 105 S.Ct. 1504, 1512, 84 L.Ed.2d 518 we affirm the district judge’s decision to deny Ant-zoulatos’ credit for acceptance of responsibility. The district court thoroughly examined the various factors noted in Application Note 1 to Section 3E1.1, including the fact that Antzoulatos did not voluntarily withdraw from criminal conduct, and that Antzoulatos’ plea was made on the day of trial. Most significantly, the Court considered Antzoulatos’ written letter to the Court to be unbelievable:
But repeatedly, and more importantly as I read through here, he excuses himself. * * * [H]e says he spent most of his time purchasing his own vehicles and not paying any attention to what Farrow and Jackson were doing, even though they purchased a Rolls Royce at that auction. * * * [H]e has a relationship with an individual which * * * gives him 50 percent of the profits of certain customers, at the same time claiming that he didn’t know what type of business he was engaged in. * * * I have been asked to accept a lot of unusual stories, but this one is more than I can swallow.
Tr. at 24-26. These findings are not clear error.
For the foregoing reasons, we Affirm the sentence of Dennis G. Antzoulatos.
. Counts two through four, charging Antzoula-tos with aiding and abetting various substantive violations of 18 U.S.C. § 1956(a)(1)(B), were dismissed pursuant to the plea agreement entered into by Antzoulatos.
. The statute also defines some of the terms used above:
(1) The term "knowing that the property involved in a financial transaction represents the proceeds of some form of unlawful activity” means that the person knew the property involved represented proceeds from some form, though not necessarily which form, of activity that constitutes a felony * * *.
(2) The term "conducts" includes initiating, concluding, or participating in initiating, or concluding a transaction.
(3) The term "transaction” includes a purchase, sale, loan, pledge, gift, transfer, delivery, or other disposition * * *.
(4) The term "financial transaction” means (A) a transaction (i) involving the movement of funds by wire or other means or (ii) involving one or more monetary instruments, which in any way or degree affects interstate or foreign commerce * * *.
(5) The term “monetary instruments” means (i) coin or currency * * * personal checks, bank checks, and money orders * * *. 18 U.S.C. § 1956(c)(l)-(5). Additionally, the term "specified unlawful activity" is defined in Section 1956(c)(7) and encompasses a lengthy list of crimes, including, by reference to Section 1961(1) of Chapter 18, any offense relating to the "felonious manufacture, importation, receiving, concealment, buying, selling, or otherwise dealing in narcotic or other dangerous drugs.”
. The statute’s legislative history confirms that more than mere suspicion is required on the merchant's part. An earlier version of the provision at issue contained "reason to know” and "reckless disregard” standards; this language was replaced in response to concerns raised by several witnesses during hearings on the bill. S.Rep. No. 433, 99th Cong., 2d Sess. 6-8 (1986). The report continues,
The "knowing” scienter requirements are intended to be construed, like existing "knowing" scienter requirements, to include instances of "willful blindness.” * * * [A]n automobile dealer who sells a car at market rates to a person whom he merely suspects of involvement with crime, cannot be convicted of this offense in the absence of a showing that he knew something more about the transaction or the circumstances surrounding it.
Id. at 9-10.
The Second Circuit has noted' that the plain meaning of the statute requires a "knowing” mental state rather than mere recklessness or negligence. United States v. Lora, 895 F.2d 878, 880 n. 2 (2d Cir.1990).
. The mistitling of cars is relevant in this case only because of the number of incidents involved and only then when viewed in conjunction with the other facts of this case. There is certainly nothing illegal about buying a car and placing that car in someone else’s name; parents do it frequently for their children. The Tenth Circuit in United States v. Sanders, 929 F.2d 1466, 1472-1473 (10th Cir.1991), certiorari denied, — U.S. —, 112 S.Ct. 143, 116 L.Ed.2d 109, overturned a money laundering conviction that was based on the purchase of two cars using drug proceeds, one of which was titled in the name of the drug dealer’s daughter. These two transactions were held insufficient to show a purpose of concealment, especially when the daughter was physically present at the purchase of the car placed in her name. Antzoulatos’ case is different because of the number of transactions he engaged in involving mistitling, and because many of the cars were titled in fictional names or the name of his company. Cf. United States v. Gurary, 860 F.2d 521, 526-527 (2d Cir.1988) (upholding conscious avoidance instruction for defendant charged with aiding preparation of fraudulent tax returns where defendant was involved in hundreds of transactions, but implying a different result if only a single transaction had been involved), certiorari denied, 490 U.S. 1035, 109 S.Ct. 1931, 104 L.Ed.2d 403.