
    UNITED STATES of America, Plaintiff-Appellee, v. James R. TURCOTTE, Defendant-Appellant.
    No. 03-2988.
    United States Court of Appeals, Seventh Circuit.
    Argued Nov. 1, 2004.
    Decided April 19, 2005.
    Rehearing and Suggestion for Rehearing En Banc Denied June 14, 2005.
    
      Monika Bickert (argued), Office of the United States Attorney, Chicago, IL, for Plaintiff-Appellee.
    Derek J. Sarafa (argued), Winston & Strawn, Chicago, IL, for Defendant-Appellant.
    Before CUDAHY, ROVNER and WOOD, Circuit Judges.
   CUDAHY, Circuit Judge.

Appellant James Turcotte was convicted of three counts of violating the Controlled Substances Act, including a conviction for possession and distribution of a controlled substance analogue as defined by 21 U.S.C. § 802(32). Turcotte now appeals his conviction before this Court, alleging that (1) the district court issued at least two erroneous and prejudicial jury instructions relating to the Analogue Provision of the Controlled Substances Act, (2) the prosecution improperly withheld Brady material at trial, (3) his conviction was precluded by existing federal law, (4) the Analogue Provision of the Controlled Substances Act is unconstitutionally vague and (5) the district court made several errors in trial management. We now affirm.

I. BACKGROUND

In this case we confront Congress’s attempt to adapt the nation’s controlled substances laws to the dizzying pace of innovations in drug technology. This case also marks the most recent chapter in one man’s ill-fated personal and professional odyssey from bricklayer to bodybuilder to drug merchant. James Turcotte worked as a bricklayer throughout most of the 1990s. In late 1998 or early 1999, Tur-cotte was contacted by Brian Gore and asked to do some construction work at Max Muscle, a store selling vitamins, supplements, sports apparel and weightlifting equipment in a shopping mall in Downers Grove, Illinois. Max Muscle had been recently opened by Gore’s friend Scott Wright. In September, 1999, Turcotte participated in a bodybuilding contest sponsored by Max Muscle, which required contestants to use Max Muscle products while preparing for the competition. In conjunction with this competition, Turcotte purchased nutritional supplements from Max Muscle, including “Verve 5.0,” a purported vitamin' supplement that contains the chemicals GHB, GBL and BD.

Sometime in March 2000, Gore sold Best Buy Supplements, an internet-based company through which Turcotte was to sell Verve 5.0, to Turcotte. Best Buy Supplements conducted its business through the websites bestbuysupplements.com and growthhormoneshop.com, offering a variety of bodybuilding and fitness products including Verve 5.0 and other “Growth Hormone Products.” The bestbuysupple-ments.com website, which listed Turcotte as its “owner,” touted Verve 5.0 as the “absolute finest quality GHB precursor” and acknowledged that both “furanone”— another name for GBL — and “butanediol” (BD) are “illegal nationwide.” To fulfill customer orders, Turcotte purchased cases of Verve labeled “cleaning supplies.”

In August of 2000, the Drug Enforcement Administration (DEA) began an undercover investigation of Turcotte’s sales of Verve after arresting Kevin Masquida, who had purchased Verve online from Best Buy Supplements. Masquida entered into a plea agreement with the government under which he agreed to help the DEA arrange an undercover purchase of Verve from Turcotte. After a series of phone calls from Masquida, the purchase was scheduled for 5:00 p.m. on September 8, 2000, at a Shell gas station in Mokena, Illinois. Masquida agreed to buy twenty cases of Verve for $10,000.

On the day of the transaction, undercover DEA agent Robert Coleman accompanied Masquida, posing as an individual interested in purchasing Verve. The entire transaction was monitored by DEA surveillance. Turcotte and Gore met Masqui-da and Coleman at the Shell station as planned, and they drove to a nearby Wendy’s parking lot where Turcotte had parked his van. ' Coleman handed Turcotte a styrofoam cup containing $10,000 in cash, and Turcotte directed the group to transfer 20 cases of Verve from Turcotte’s van to Masquida’s van. When ' the transfer began and Coleman was able to confirm that the cases did contain Verve, DEA agents arrived to arrest Turcotte and Gore.

Turcotte was charged on three counts of a five-count indictment. Count One charged Turcotte with knowingly and intentionally conspiring to defraud and mislead the government by introducing mis-branded drugs (GHB, GBL and BD) into interstate commerce. Count Two charged Turcotte with conspiring to possess and distribute GHB (a Schedule I Controlled Substance), GBL (a Schedule I controlled substance analogue under 21 U.S.C. § 802(32)), and BD (a Schedule I controlled substance analogue under § 802(32)) in violation of the Controlled Substances Act (CSA or “the Act”), 21 U.S.C. §§ 841(a)(1) and 813. Count Five charged Turcotte with knowingly and intentionally possessing with intent to distribute 60 gallons of GHB and GBL in violation of §§ 841(a)(1) and 813 of the CSA. As to GBL and BD, these charges come under the Analogue Provision of the Controlled Substances Act, 21 U.S.C. § 802(32), which provides that substances satisfying the definition of a “controlled substance analogue” may be regulated as controlled substances even though they are not formally classified as such under federal law.

On November 12, 2000, Turcotte proceeded to trial. Government witnesses included Agent Coleman, Masquida, officials from the Food and Drug Administration (FDA), a forensic drug chemist from the DEA, toxicology and medical experts, registered distributors of GBL and other law enforcement and fact witnesses who testified about the physiological effects of GBL. During the trial, the government claims it suddenly became aware of Investigational New Drug Reports (INDs) which detailed research into potential medical uses for GHB, including a treatment for narcolepsy involving a new drug named Xyrem. Tur-eotte immediately requested copies of the INDs. The district court, while opining that the INDs would probably prove to be of little use to the defense, provided that the government’s witnesses would remain available for recall after presentation of the government’s case-in-chief so that Tur-cotte could cross-examine them further about the content of the new INDs. In his defense, Turcotte testified personally and also called his own forensic chemistry and medical experts to testify. Turcotte admitted that he knew Verve was a chemical solvent and that he had sold it for human consumption.

At the conclusion of the trial, the district court issued its instructions to the jury. Two of them are at issue here. First, with regard to the definition of a controlled substance analogue, the district court instructed the jury that the three clauses of the CSA’s Analogue Provision, 21 U.S.C. § 802(32), should be read in the disjunctive rather than the conjunctive. After acknowledging that the Seventh Circuit had not yet endorsed either reading of the provision, the court gave the jury special verdict forms on which they could rule specifically on each of the Analogue Provision’s three clauses. The court explained that it would temporarily defer ruling on the proper reading of the Act but would revisit the issue if the special jury forms revealed that the different readings of the provision — conjunctive versus disjunctive — would have produced different results. Second, with regard to Count Five, the district court instructed the jury on the scienter requirement of the CSA’s analogue provision, telling jury members they could convict Turcotte even if they did not find that he knew GBL was a “controlled substance.”

On November 22, 2002, the jury convicted Turcotte on all counts, returning special verdict forms finding that GBL met all three criteria listed in the CSA’s Analogue Provision, 21 U.S.C. § 802(32), but that BD met only one of these criteria. On January 22, 2003, Turcotte timely filed a motion for a judgment of acquittal or a new trial. He claimed that (1) the district court’s jury instruction mandating a disjunctive reading of the CSA’s Analogue Provision was error, (2) the court’s jury instruction regarding the Analogue Provision’s scienter requirement was erroneous, (3) the prosecution improperly withheld Brady materials (the new INDs) and (4) the Analogue Provision of the CSA is unconstitutionally vague. Turcotte later filed an untimely motion further alleging (1) that GBL and BD are not controlled substance analogues of GHB because GHB is no longer a Schedule I Controlled Substance, and (2) that the Dietary Supplements Health & Education Act (DSHEA) prevents BD and GBL from being classified as controlled substance analogues.

The district court considered all of Tur-cotte’s claims — timely and untimely alike— and denied his post-trial motions for an acquittal or a new trial in a memorandum disposition dated July 7, 2003. United States v. Turcotte, 286 F.Supp.2d 947 (N.D.Ill.2003). Turcotte was sentenced to 54 months’ imprisonment for each of the three counts (to run concurrently), three years’ supervised release and a fine. Turcotte now appeals the district court’s denial of his post-trial motions and asks that his conviction be reversed, or, in the alternative, that the case be remanded for re-sentencing.

II. JURISDICTION

Since Turcotte was charged with a violation of the federal Controlled Substances Act (21 U.S.C. §§ 841(a)(1) and 846), the district court had jurisdiction pursuant to 18 U.S.C. § 3231, which provides for district court jurisdiction over “all offenses against the laws of the United States.” The jury returned a guilty verdict against Turcotte on November 22, 2002, and the district court entered judgment on July 22, 2003. Turcotte timely filed his Notice of Appeal on July 23, 2003, and this Court now has jurisdiction to review the final order of the district court pursuant to 28 U.S.C. § 1291.

III. DISCUSSION

Turcotte advances six distinct claims in his challenge to the district court’s ruling below. We address each of these claims in turn.

A. Conjunctive Versus Disjunctive Readings of the CSA’s Analogue Provision

The particular constructional issue raised here is one of first impression for this Court. The CSA provides that certain substances, while not officially scheduled as controlled substances themselves, may be regulated as such if they meet the definition of a “controlled substance analogue.” The CSA defines a “controlled substance analogue” as “a substance — ”

(i) the chemical structure of which is substantially similar to the chemical structure of a controlled substance in schedule I or II;
(ii) which has a stimulant, depressant, or hallucinogenic effect on the central nervous system that is substantially similar to or greater than the stimulant, depressant or hallucinogenic effect on the central nervous system of a controlled substance in schedule I or II; or
(iii) with respect to a particular person, which such person represents or intends to have a stimulant, depressant, or hallucinogenic effect on the central nervous system that is substantially similar to or greater than the stimulant, depressant, or hallucinogenic effect on the central nervous system of a controlled substance in schedule I or II.

21 U.S.C. § 802(32)(A) (2004).

As the old adage instructs, the devil is in the details — the relevant detail here being the single word “or” between clauses (ii) and (iii) of the definition. There are two possible readings of this definition. Under a disjunctive reading, a substance that satisfies any one of these three criteria qualifies as a controlled substance analogue. Under a conjunctive reading, the provision requires two things: (1) The substance in question must have a chemical structure substantially similar to a controlled substance (criterion one) and (2) it must either have a substantially similar effect on the central nervous system (criterion two) or be purported or intended to have such an effect (criterion three).

Both parties and the district court agree that the Seventh Circuit has yet to address this particular constructional issue. See 286 F.Supp.2d at 951. It is also undisputed that the district court submitted a disjunctive instruction to the jury with the intention of revisiting the issue if the special verdict forms showed that the two interpretations would lead to different results. In its disposition of Turcotte’s motion for a post-trial acquittal or a new trial, the district court stated that it was actually “inclined to agree” with Turcotte’s arguments for a conjunctive reading of the Act, but that “such a determination ... does not affect defendant’s conviction” since “[t]he jury’s special verdict forms establish that the government proved all three elements of Section 802(32)(A) beyond a reasonable doubt with respect to GHB.” Id. On appeal, the parties differ on the correctness of the district court’s disjunctive instruction and its effect (or lack thereof) on Mr. Turcotte’s conviction and sentencing. Turcotte contends that the district court’s instruction was erroneous, and that it did indeed affect his ultimate sentence. This Court reviews de novo a district court’s denial of a requested jury instruction. United States v. Slater, 348 F.3d 666 (7th Cir.2003).

Unfortunately, the text of the Controlled Substances Act analogue provision is not a model of clarity. Common sense and the practical implications of various interpretive options ultimately offer more guidance than the text and structure of § 802(32)(A) itself. As a matter of strict textual analysis, § 802(32)(A) is susceptible to either a disjunctive or a conjunctive reading. The word “which” in the beginning of clauses (ii) and (iii) could be construed to refer either to “substance” in the preface of the definition (favoring a disjunctive reading) or to “chemical structure” in clause (i) (favoring a conjunctive reading). Yet the vast majority of federal courts to confront this issue have adopted the conjunctive reading. United States v. Hodge, 321 F.3d 429, 433 (3d Cir.2003) (presenting in-depth analysis of the plain meaning and legislative history of § 802(32)(A)); United States v. Klecker, 348 F.3d 69, 71 (4th Cir.2003) (adopting the conjunctive reading); United States v. Washam, 312 F.3d 926, 930 n. 2 (8th Cir.2002) (adopting the conjunctive reading); United States v. McKinney, 79 F.3d 105, 107-08 (8th Cir.1996), vacated on other grounds, 520 U.S. 1226, 117 S.Ct. 1816, 137 L.Ed.2d 1025 (1997) (presenting the test in the conjunctive without further elaboration); United States v. Brown, 279 F.Supp.2d at 1240 (S.D.Ala.2003) (adopting the conjunctive reading); United States v. Vickery, 199 F.Supp.2d at 1371 (N.D.Ga.2002) (same); United States v. Clifford, 197 F.Supp.2d at 519-20. (E.D.Va.2002) (same); United States v. Forbes, 806 F.Supp. 232, 235 (D.Colo.1992) (reviewing the Act’s legislative history and asserting that the conjunctive reading is required to prevent absurd results). See also United States v. Roberts, 363 F.3d 118, 121 (2d Cir.2004) (briefly surveying the relevant precedents and accepting the conjunctive reading), The only arguable exceptions are United States v. Fisher, 289 F.3d 1329, 1338 (11th Cir.2002), in which the Eleventh Circuit expressly declined to decide the issue, and United States v. Granberry, 916 F.2d 1008, 1010 (5th Cir.1990), in which the Fifth Circuit recited the test in the disjunctive without discussion or elaboration.

The majority of these courts base their rulings largely on the absurd results that might obtain under a disjunctive reading, noting that alcohol and caffeine could be criminalized as controlled substance analogues based solely on the fact that, in concentrated form, they might' have depressant or stimulant effects similar to illegal drugs. See, e.g., Forbes, 806 F.Supp. at 235. Similarly, the sale of everyday substances could be criminalized if the seller merely represents that they are banned substances or have physiological effects similar to illegal drugs. See id. (noting that under a disjunctive reading, the sale of powdered sugar could be criminalized if the seller represents that it is cocaine); Hodge, 321 F.3d 429 (rejecting a disjunctive approach and holding that selling a mixture of wax and flour is not criminalized merely because the seller represented it to be “crack cocaine”).

Moreover, the legislative history of the Act suggests that such bizarre consequences were not intended by Congress. The Act was intended primarily to prevent scientists from slightly modifying the chemical structure of banned drugs to create new “designer drugs” that would have similar physiological effects but would not be covered by the law’s controlled substances schedules. See, e.g., Hodge, 321 F.3d 429 (conducting an extensive review of the Act’s legislative history). According to one court, there is “not a scintilla of evidence” that “Congress intended to cover and criminalize sales of legal substances such as flour, salt, ginseng, vitamin B, etc., merely because the seller represents that they will yield a stimulant, depressant, or hallucinogenic effect like that of a controlled substance.” Clifford, 197 F.Supp.2d at 520-21. The court in Clifford also pointed out that Congress is capable of indicating an unambiguous disjunctive intent when it so desires: In at least one other provision of this very Act (§ 802(9)), a number of subordinate causes are listed in a fashion similar to § 802(32)(A), but each subsection is separated by the word “or” to indicate a clear disjunctive intent. Id. at 519-20.

Given that the text of the Act does not clearly demand either reading, we find the practical policy considerations identified by our sister courts compelling, especially when coupled with the Act’s overall structure and legislative history. We therefore elect to heed the call of both accumulated precedent and common sense, joining the vast majority of federal courts in adopting the conjunctive reading of § 802(32)(A). Accordingly, the district court’s disjunctive jury instruction was error. However, as will be discussed presently, this error was not ultimately prejudicial to Turcotte.

The parties’ dispute over the import of the district court’s disjunctive jury instruction seems to reflect fundamentally different readings of the jury’s special verdict forms and the Presentence Investigation Report. Turcotte alleges that the jury found BD to be an analogue of GHB based on the fact that it satisfied only clause two of § 802(32)(A) (similar effect on the nervous system), and that therefore, since his conviction and sentence as to possession and distribution of BD was based on an erroneous disjunctive reading of the Act, he is entitled to relief in this Court.

The government responds by arguing that, since the jury found BD to satisfy only clause two of § 802(32)(A), Turcotte was not convicted or sentenced for possession or distribution of BD at all. In effect, the government alleges that the jury and the probation officer preparing the Presen-tence Investigation Report read § 802(32)(A) conjunctively, notwithstanding the district court’s disjunctive instruction. The government claims that Tur-cotte’s sentence was based purely on his possession and distribution of GBL, which the jury found satisfied all three clauses of § 802(32)(A) (and thus would have qualified as an analogue of GHB under either a disjunctive or conjunctive reading of the Act).

The written record favors the government on this point. Turcotte’s claims here seem to be moot. First, it is important to note that, by them own terms, Turcotte’s arguments on this issue relate only to BD; both parties agree that the jury found GBL to meet all three clauses of § 802(32)(A), and thus that Turcotte would have been convicted for possession and distribution of GBL under either reading of the statute. As such, Turcotte’s claims here only have traction if he was indeed convicted of possession with intent to distribute BD (as an analogue of GHB) and separately sentenced for this offense. The Presentencing Investigation Report reveals that Turcotte’s conviction did not rest on his possession or distribution of BD, and it unequivocally states that his possession and distribution of BD did not affect calculation of his sentence. While the Report initially states that Turcotte was convicted of “conspiring with Brian Gore to possess with the intent to'distribute, and possessing with the intent to distribute, GHB, GBL, and BD,” it later makes clear that the jury did not find BD to be a controlled substance analogue and, accordingly, that Turcotte’s possession of BD did not play any role in his conviction or sentencing:

With specific regard to BD (1,4 Butane-diol), the jury has returned a special verdict which states that BD is not a Schedule I Narcotic Drug Controlled Substance analogue, because BD’s chemical structure is not significantly similar to the chemical structure of GHB. Thus the amounts of Flower Power (BD) and any other substances which contained BD are not included in the amounts of controlled substances for which the defendant is accountable, notwithstanding his possession and distribution of said substances.

(emphasis added). The Report then went on to state that even “[i]f the Court were to rule that BD is a controlled substance analogue of GBL, a Schedule I depressant, in contravention of the jury’s special verdict, the number of units of BD involved in this casé ... would not increase the base offense level applicable to this offense.” (emphasis added).

No matter how one looks at it, BD simply does not appear to have been factored into Turcotte’s sentencing. Thus the district court’s disjunctive jury instruction, while erroneous, cannot be s.aid to have prejudiced Turcotte. In fact, the district court seems to presage this ruling in its order denying Turcotte’s post-trial motion for a judgment of acquittal or a new trial, stating that it was actually “inclined to agree” with Turcotte’s arguments for a conjunctive reading of the Act, but that “such a determination ... does not affect defendant’s conviction.” 286 F.Supp.2d at 951. Given the prior absence of a clear ruling on the issue in this circuit, the district court’s decision to have the jury rule separately on each element .of the Analogue Provision appears an appropriate jurisprudential precaution. As such, we have no occasion to reverse the district court’s ruling on this narrow constructional issue, though we hereby serve notice that courts in this circuit should henceforth apply a conjunctive reading of the CSA’s Analogue Provision.

B. The District Court’s Instructions on Scienter

Turcotte next alleges that the district court improperly instructed the jury that they could convict him under § 841(a) even if he did not know that GBL was an illegal controlled substance analogue. In proceedings below, the district court gave the following instruction:

To sustain the charge in Count Five of possessing with intent to distribute mixtures containing a controlled substance, the government must prove the following propositions: First, the defendant knowingly and intentionally possessed mixtures containing GBL; Second, the defendant possessed mixtures containing GBL with the intent to deliver it to another person; and Third, that mixtures containing GBL are an analogue of GHB, a Schedule I Controlled Substance. It does not matter whether the defendant kneiv the substance was a controlled substance, only that it was a mixture containing GBL.

(emphasis added). We review de novo a district court’s denial of a requested jury instruction. See Slater, 348 F.3d 666.

The district court and the government argue for application of the time honored maxim that “ignorance of the law is no excuse.” They contend that § 841(a) does not require knowledge that the substance in question is a controlled substance — a defendant must merely know the identity of the substance being possessed and distributed. See 286 F.Supp.2d at 951. The district court expresses some doubt about this conclusion however, conceding “[p]er-haps that goes too far, as it might, possibly, in other circumstances, ensnare individuals engaged in apparently innocent conduct.” Id. Nonetheless, the government and the district court stand firm, maintaining that even if knowledge of a substance’s illegality is required under the Act, the special jury forms used in this case resolve the issue, as they indicate the jury found that Turcotte “represented or intended” that GBL had physiological effects “substantially similar to or greater than” GHB, a controlled substance in Schedule I.

Such a position is extremely problematic, however, since the Analogue Provision imposes criminal liability through the more general provisions of the CSA, 18 U.S.C. § 841(a), which implicate a well-established scienter requirement. This Court has previously held — on multiple occasions — that as a prerequisite to liability for possessing a controlled substance with intent to distribute under § 841(a), defendants must know that the substance in question is a controlled substance. United States v. Barlow, 310 F.3d 1007, 1012 (7th Cir.2002) (“Section 841(a) requires only that defendant know that he possesses a controlled substance; it does not require that he know the type of controlled substance he possesses.”); Lanier v. United States, 220 F.3d 833, 840 (7th Cir.2000) (requiring “knowledge that [the drug] is a controlled substance”); U.S. v. Jones, 248 F.3d 671, 675 (7th Cir.2001) (citing Lanier for the same rule). In fact the Seventh Circuit Pattern Jury Instructions articulate the same standard: “It is sufficient that the defendant knew that the substance was some kind of prohibited drug. It does not matter whether the defendant knew the substance was [a specific drug].” STAR Modern Federal Jury Instructions — Criminal, § 7-202-03, 21 U.S.C. § 841(a)(1) (2004).

Yet these precedents read awkwardly in the context of the present case, since they assume the paradigmatic drug case in which the substances involved are per se illegal — substances such as cocaine, heroin and the like. All of the aforecited Seventh Circuit cases involve prosecutions for per se illegal drugs like cocaine base (Barloiv), marijuana (Lanier) and crack cocaine {Jones). In such cases, knowledge of the specific substance involved will usually automatically imply knowledge that the substance is controlled. Or, even if the distributor of the substance does not know its specific identity, he or she is at least aware that it is a controlled substance. See, e.g., Barlow, 310 F.3d at 1012. Here, and in other analogue cases under § 802(32)(A), the opposite is true — many newly engineered and relatively unknown substances may be involved such that knowledge of the substance’s .identity does not automatically imply knowledge of its status as a controlled substance. Indeed new “designer drugs” are often created as alternatives to known illegal drugs precisely because they may be sold with an appearance of legality. Unable to keep its controlled substance schedules current in the face of accelerating innovations in drug technology, Congress enacted the Analogue Provision to target distribution .of just such substances.

And therein lies the rub. The CSA requires a showing of scienter, but the exact contours of this requirement are not obvious in the context of the Analogue Provision. At least one court has ruled that “the definition of controlled substance analogue does not require any scienter — a defendant does not have to ‘know’ that a substance has a substantially similar chemical structure to an illegal drug.” Forbes, 806 F.Supp. at 238. See also United States v. Carlson, 87 F.3d 440, 443 n. 3 (11th Cir.1996) (citing Forbes and noting “the absence of a scienter requirement in the Analogue Act”). Other courts have applied the more general scienter requirement of the CSA, 18 U.S.C. § 841(a), holding that the Analogue Provision “requires the Government to show that the defendants knew that they possessed a controlled substance.” Roberts, 363 F.3d at 123 n. 1. Under this construction, defendants “need not know the exact nature of the drug; it is sufficient that they be aware that they possessed ‘some controlled substance.’ ” Id. (citing United States v. Morales, 577 F.2d 769, 776 (2d Cir.1978)). Neither of these approaches seems especially satisfying.

In this particular context, applying the standard requirement that a defendant must know the substance in question is a “controlled substance” is nonsensical since controlled substance analogues are, by definition, not “controlled substances” — their distribution is criminalized, despite their omission from the government’s controlled substances schedules, because they have similar Chemical structures and either actually or purportedly similar physiological effects to controlled substances. A substance’s legal status as a controlled substance analogue is not a fact that a defendant can know conclusively ex ante; it is a fact that the jury must find at trial (applying the three clauses of the Analogue Provision). Direct and literal application of the scienter requirement applicable to § 841(a), in other words, would threaten to eviscerate the Analogue Provisions of § 802(32)(A) at one stroke.

On the other hand, doing away with the scienter requirement altogether could, as the district court realized, “ensnare individuals engaged in apparently innocent conduct.” 286 F.Supp.2d at 951. Such a construction also would make the Analogue Provision more vulnerable to vagueness challenges. See Village of Hoffman Estates v. Flipside Hoffman Estates, Inc., 455 U.S. 489, 499, 102 S.Ct. 1186, 71 L.Ed.2d 362 (1982) (“[A] scienter requirement [in a criminal statute] may mitigate a law’s vagueness, especially with respect to the adequacy of notice to the complainant that his conduct was proscribed.”); Roberts, 363 F.3d at 123 (“Because the statute at issue here contains a scienter requirement ... the defendants’ vagueness challenge must be met with some measure of skepticism”). Discarding the scienter requirement would essentially mean that individuals deal in narcotics substitutes at their own risk, removing a primary mens rea element of possession and distribution offenses.

In light of all these considerations, we feel that our precedents demand a showing that the defendant knew the substance in question was a controlled substance analogue. That is, the defendant must know that the substance at issue meets the definition of a controlled substance analogue set forth in § 802(32)(A): A defendant must know that the substance at issue has a chemical structure substantially similar to that of a controlled substance, and he or she must either know that it has similar physiological effects or intend or represent that it has such effects. We recognize that requiring the government to prove scienter as to these criteria may impose a significant prosecu-torial burden in some cases. The question of similar chemical structure is particularly nettlesome since, even if such chemical similarities exist, and even if the defendant is aware of these similarities, the intricacies of chemical science may render it extremely difficult to prove that a defendant had such knowledge. As a provisional remedy for this problem, we prescribe that, in such cases, if the scienter requirement is met with regard to the second part of the analogue definition (knowledge or representation of similar physiological effects), the jury is permitted — but not required — to infer that the defendant also had knowledge of the relevant chemical similarities.

This approach is justified since, as a practical matter, defendants who know or represent to others that the substance in question has physiological effects similar to a controlled substance are likely to be aware of basic chemical similarities as well, even if that fact is difficult to prove conclusively. This approach also dovetails with the commonsense recognition that, in selling or purchasing such substances, all parties to the transaction are primarily interested (perhaps solely interested) in the substance’s physiological effects. Yet at the same time, if the defendant truly had no knowledge of the substance’s chemical character, or if, under the circumstances, chemical complexities make such knowledge extremely unlikely, an avenue should be left open for defendants to refute such an inference. In any case, our well-established jurisprudence regarding the scien-ter requirements of controlled substances violations require that juries confront these questions of knowledge squarely.

The district court, while acknowledging that the scienter requirement implied by its own jury instruction “[pjerhaps goes too far,” maintains that its jury instructions were non-prejudicial since the jury specifically determined that Turcotte represented or intended that GBL had physiological effects similar to GHB. 286 F.Supp.2d at 951. However, as just discussed, while such a determination suffices to demonstrate scienter with respect to the second prong of the analogue definition (actual or intended similar physiological effect), it is not equivalent to finding knowledge of actual chemical similarity. One could represent to others (earnestly or not) that a substance has physiological effects similar to a controlled substance despite being totally ignorant of its actual chemical properties. Turcotte’s representations as to the physiological effects of GBL do support an inference that such knowledge existed, but the jury did not confront this question directly below. Given the evidence adduced at trial, it appears a jury certainly could have determined that Turcotte had the requisite knowledge to trigger liability under § 802(32)(A) (though the evidence does not compel such a conclusion). However, the jury was specifically instructed to forego this determination. The district court’s instructions as to scienter were thus, at best, incomplete and, at worst, highly misleading as to the prerequisites for liability under the Analogue Provision.

Ordinarily such shortcomings might amount to reversible error, but in the present case we find any deficiencies in the district court’s scienter instructions harmless. The jury specifically found that Turcotte knew the substance he possessed contained GBL, and unlike many other potential controlled substance analogues, Congress has specifically identified GBL as an analogue of GHB. See United States v. Ansaldi, 372 F.3d 118, 123 (2d Cir.2004) (“GBL is one of the substances that the statute actually identifies as a potential controlled substance analogue.”); United States v. Fisher, 289 F.3d at 1336 (noting that “statements found in Public Law 106-172 and the DEA’s Final Rules indicate that both Congress and the DEA considered GBL to be an analogue of GHB.”).

In amending the Controlled Substances Act to include GHB, Congress declared that “[i]f taken for human consumption, common industrial chemicals such as gamma butyrolactone [GBL] and 1,4-butane-diol [BD] are swiftly converted by the body into GHB. Illicit use of these and other GHB analogues and precursor chemicals is a significant and growing law enforcement problem.” Pub. Law No. 106-172, § 2(4) (2000) (emphasis added). DEA regulations also specify that “GBL and 1,4-butanediol are structurally and pharmacologically similar to GHB and are often substituted for GHB. Under certain circumstances they may satisfy the definition of a controlled substance analogue.” Placement of Gamma-Butyrolac-tone in List I of the Controlled Substances Act, 65 Fed.Reg. 21,645-47 (April 24, 2000) (emphasis added). As the Second Circuit asserted in Ansaldi, “[r]egardless of any other ways in which the laws governing controlled substance[s] might be vague, there is one thing they make perfectly clear—the sale of GBL for human consumption is illegal.” 372 F.3d at 122. Cf. United States v. Washam, 312 F.3d 926, 931 (8th Cir.2002) (holding that these Congressional pronouncements also confirm BD’s status as a controlled substance analogue).

In our view such pronouncements are sufficient to put any drug merchant on notice that GBL qualifies as a controlled substance analogue. Thus having acknowledged that he knew he was selling substances containing GBL, Turcotte cannot then turn around and claim that he had no knowledge of GBL’s- status as an analogue of GHB. As with other known controlled substances (including GHB), knowledge of the substance’s specific identity implies knowledge of the substance’s legal status. Ignorance of the relevant legal provisions is no defense. See Ansaldi, 372 F.3d at 128 (holding that defendants’ belief that “they were breaking no law by selling GBL” does not constitute a defense); United States v. Desurra, 865 F.2d 651, 653 (5th Cir.1989) (similar holding).

Applied to any other controlled substance analogue, an instruction such as the one given here might well warrant reversal of a conviction. However, given the clear Congressional and regulatory pronouncements of the status of GBL, any error in the district court’s scienter instructions was harmless. Accordingly, we affirm the ruling of the district court on this issue.

C. The Brady Claim

Turcotte next claims that the prosecution violated his rights under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), by improperly withholding FDA Investigational New Drug Applications (INDs) during the trial. Brady instructs that the prosecution has an affirmative duty to disclose all information that is (1) in the government’s possession, (2) material and (3) exculpatory. United States v. Bhutani, 175 F.3d 572, 576 (7th Cir.1999); United States v. Hartbarger, 148 F.3d 777, 786 (7th Cir.1998). Under our precedents, any evidence whose “suppression undermines confidence in the outcome of the trial is considered material.” United States v. Gonzalez, 93 F.3d 311, 316 (7th Cir.1996) (quotations omitted). Crucially, district courts have broad discretion in determining Brady violations, and so this Court reviews the decision below only for abuse of discretion. United States v. Knight, 342 F.3d 697, 705 (7th Cir.2003) (“The district court maintains broad discretion to determine Brady violations; we will review the exercise of that discretion for abuse only.”); United States v. Wilson, 237 F.3d 827 (7th Cir.2001) (same rule).

In the decision below, the district court ruled that the government disclosed the INDs “promptly after learning of their existence” such that “[d]efense attorneys were ... able to review the material and use it during the trial.” 286 F.Supp.2d at 951. The district court further determined that the INDs contained no real exculpatory information and that any government delay in producing the materials did not undermine confidence in the outcome of the trial. Id. Turcotte, on the other hand, claims that the government was 18 months late in disclosing the INDs, and that the INDs were exculpatory since they contained information that contradicted the testimony of government expert witnesses regarding the harmful effects of GHB, including FDA approval of Xyrem, a drug used for treating narcolepsy that contains GHB. Turcotte claims that because of the government’s tardy disclosure, his own expert witnesses did not have sufficient time to review these INDs and thus that he was not able to present this exculpatory evidence at trial.

If only Turcotte had bought and distributed Xyrem to treat narcolepsy, he might have a colorable claim. As it is, his Brady claim fails. It is undisputed that the government did disclose the material in question, albeit somewhat later than it ought, and the district court determined that Turcotte had sufficient time to review the materials and use them in his defense. The district court also allowed Turcotte to recall government expert witnesses after presentation of the prosecution’s case in chief and cross-examine them as to information contained in the INDs, though Turcotte apparently declined to do so.

Lastly, even if the INDs contain the information that- Turcotte alleges, they do not change the fact that GHB was a Schedule I controlled substance at the time of Turcotte’s alleged conduct, that GBL was found by the jury to be an analogue of GHB and that Turcotte sold GBL for impermissible purposes. The other medical uses of GHB allegedly described in the INDs are not particularly relevant to Turcotte’s conduct or to the facts of this case. That GHB may have been approved for another use as a component of some other drug does not alter the fundamental basis of Turcotte’s liability. The district court has broad discretion in identifying Brady violations, and nothing in the record suggests that the district court abused this discretion. We therefore affirm the ruling of the district court rejecting Turcotte’s Brady claim.

D. The Vagueness Claim

Turcotte’s final major claim is that the Analogue Provision of the CSA is unconstitutionally vague in that “it fails to provide fair notice to the public regarding what substances are ‘analogues’ and therefore prohibited.” Under Kolender v. Lawson, a penal statute is void for vagueness if it does not define an offense with sufficient clarity to allow people of ordinary intelligence to understand what conduct is prohibited or if it is so vague as to allow for arbitrary or discriminatory enforcement. 461 U.S. 352, 357, 103 S.Ct. 1855, 75 L.Ed.2d 903 (1983). Tureotte claims that the term “substantially similar” in § 802(32)(A) is too vague to advise people of ordinary intelligence as to which substances qualify as controlled substance analogues. The district court disagreed, ruling that “a person of ordinary intelligence should recognize the similarity between GBL and GHB, and that Section 802(32)(A) is not unconstitutionally vague.” 286 F.Supp.2d at 951-52 (citing Fisher, 289 F.3d at 1338-39). We review de novo a challenge to the constitutionality of a federal statute. United States v. Vallejo, 373 F.3d 855, 859 (7th Cir.2004).

In support of his contention, Tureotte claims there is no scientific consensus on the chemical similarity of GBL to GHB (while it is undisputed that the two compounds differ only by a few atoms, they are classified as different types of compounds and have different physical shapes) nor any established scientific definition of the term “substantially similar” as applied to questions of molecular chemistry. Tur-cotte also points out that several common substances either contain GHB or convert to GHB at some point in the human metabolic process, which makes the targeting of GBL and GHB essentially arbitrary.

These points are well-taken, but the relevant case law suggests that Tur-cotte faces an uphill battle. As an initial matter, we note that our ruling here confirming that the Analogue Provision carries a robust scienter requirement casts doubt on Turcotte’s vagueness challenge from the outset. Cf. Roberts, 363 F.3d at 123 (“Because the statute at issue here [§ 802(32)(A) ] contains a scienter requirement .'.. the defendants’ vagueness challenge must be met with some measure of skepticism, at least with regard to the ‘fair notice’ prong of Kolender.”) Under Supreme Court precedent, the constitutionality of an allegedly vague statutory standard “is closely related to whether that standard incorporates a requirement of mens rea.” Colautti v. Franklin, 439 U.S. 379, 395, 99 S.Ct. 675, 58 L.Ed.2d 596 (1979). Specifically, due process concerns about notice are “ameliorated” when a statute contains a scienter requirement. Hill v. Colorado, 530 U.S. 703, 732, 120 S.Ct. 2480, 147 L.Ed.2d 597 (2000).

Yet even leaving aside the implications of our scienter ruling, the Analogue Provision seems to us sufficiently clear by its own terms. The circuit courts considering this issue have unanimously held that the CSA’s Analogue Provision is not unconstitutionally vague. See, e.g., United States v. Granberry, 916 F.2d 1008, 1010 (5th Cir.1990) (ruling that the CSA’s Analogue Provision is “clearly and specifically defined, in terms readily comprehensible to the ordinary reader”); United States v. Klecker, 348 F.3d 69, 72 (4th Cir.2003); United States v. Orchard, 332 F.3d 1133, 1137-38 (8th Cir.2003); United States v. Washam, 312 F.3d 926, 930-32 (8th Cir.2002); Carlson, 87 F.3d at 443-44; United States v. Hofstatter, 8 F.3d 316, 321-22 (6th Cir.1993); United States v. Desurra, 865 F.2d 651, 653 (5th Cir.1989) (per curiam). The one contrary precedent, which Turcotte cites in support of his own arguments, is United States v. Forbes, 806 F.Supp. 232 (D.Colo.1992), in which a district court held the Analogue Provision to be unconstitutionally vague as applied to the drug AET. The court in Forbes found the Act lacking with respect to AET because “there is no scientific consensus whether AET has a chemical structure that is substantially similar to DMT or DET. The government’s own chemists cannot agree on this point .... [t]he scientific community cannot even agree on a methodology to use to determine structural similarity.” Id. at 237.

Again, Forbes is. instructive so far as it goes, but, it can be distinguished from the instant case since it involved AET rather than GBL. This distinction is crucial because no fewer than three courts of appeals have held the Analogue Provision to be sufficiently clear with respect to GBL and/or BD. In United States v. Roberts, the Second Circuit held that the Analogue Provision was not unconstitutionally vague in identifying BD as an analogue of GHB, stating that the acknowledged similarity in the chemical structures of the two compounds, combined with the fact that BD turns into GHB when ingested, are collectively sufficient to put an ordinary person on notice that BD is an analogue of GHB for purposes of the CSA. 363 F.3d at 125. The Roberts court insists that these two factors, when considered together, make the legal implications of the Analogue Provision clear with respect to BD, notwithstanding the fine-grained scientific distinctions of expert chemists. 363 F.3d at 127.

Another Second Circuit panel, convened not three months later, used this same analytical approach to conclude that “the definition of ‘controlled substance analogue’ is not unconstitutionally vague as applied to GBL.” Ansaldi, 372 F.3d at 124 (citing Roberts and pointing to “uncontro-verted testimony that GBL’s chemical structure differed from that of GHB by only three atoms” and that “GBL converted into GHB after ingestion”) (emphasis added). The Ansaldi court also points out forcefully that “GBL is one of the substances that the statute actually identifies as a potential controlled substance analogue.” 372 F.3d at 123. These same points are echoed in United States v. Fisher, where the Eleventh Circuit also held that the Analogue Provision is sufficiently clear with respect to the status of GBL. The Fisher court likewise notes that GBL converts into GHB when ingested, 289 F.3d at 1338-39, and observes that “statements found in Public Law 106-172 and the DEA’s Pinal Rules indicate that both Congress and the DEA considered GBL to be an analogue of GHB.” 289 F.3d at 1336.

Among these Congressional “statements” is the following declaration: “If taken for human consumption, common industrial chemicals such as gamma butyro-lactone [GBL] and 1,4-butanediol [BD] are swiftly converted by the body into GHB. Illicit use of these and other GHB analogues and precursor chemicals is a significant and growing law enforcement problem.” Pub. Law No. 106-172, § 2(4) (2000) (emphasis added). DEA regulations contain similar statements: “GBL and 1,4-butanediol are structurally and pharmacologically similar to GHB and are often substituted for GHB. Under certain circumstances they may satisfy the definition of a controlled substance analogue.” Placement of Gamma-Butyrolac-tone in List I of the Controlled Substances Act, 65 Fed.Reg. 21,645-47 (April 24, 2000) (emphasis added).

Admittedly, these provisions may not be using the terms “analogue” or “similar” in their technical statutory sense under the CSA, but nonetheless it is difficult indeed to claim that Turcotte lacked notice as to the chemical similarities of GBL and GHB, or as to the likelihood of being prosecuted for distribution of GBL. Indeed, Turcotte advertised Verve 5.0 as a GHB substitute on his website, which actually stated that Verve is illegal. As the Second Circuit asserted in Ansaldi, “[r]egardless of any other ways in which the laws governing controlled substance[s] might be vague, there is one thing they make perfectly clear — the sale of GBL for human consumption is illegal.” 372 F.3d at 122.

This level of clarity also speaks to the second prong of the Kolender test, which concerns arbitrary or discriminatory law enforcement. Law enforcement officials, no less than potential drug distributors, are on notice that GBL is considered an illegal analogue of GHB when sold for human consumption, and they are directed to aggressively prosecute its possession and sale. In short, it is not left to the police to arbitrarily determine the legal status of GHB, GBL or BD — Congress has spoken clearly with respect to these substances.

Given the foregoing, we affirm the district court’s ruling that the CSA is not unconstitutionally vague as applied to GBL as an analogue of GHB.

E. The Status of GBL and BD as Controlled Substance Analogues

Having assailed the district court’s jury instructions, the government’s conduct during discovery and the constitutionality of the Analogue Provision itself, Turcotte next challenges the applicability of the Analogue Provision to the substances at issue in this case. His claims on this score are essentially twofold: (1) that federal law prevents BD and GBL from being regulated, and, even if GBL and BD are subject to regulation, their status is confusing and the rule of lenity should be applied in Turcotte’s favor, and (2) that GHB was not properly scheduled as a controlled substance since its scheduling (allegedly done at the behest of the Attorney General) has expired and therefore Turcotte cannot be punished for trafficking in its chemical analogues. Both claims are frivolous and fail on their own terms.

1. The Regulation of BD and GBL as Controlled Substance Analogues Under Federal Law

Turcotte first claims that the Dietary Supplements Health and Education Act of 1994 (DSHEA), 21 U.S.C. § 321, precludes regulation of GBL and BD since both substances are dietary supplements and thus must be treated as “food” under the DSHEA. Turcotte also asserts that because GBL is a “List I chemical” under 21 U.S.C. §§ 802(33) and 802(34), pursuant to an April 2000 DEA Final Rule, GBL is not subject to regulation. These arguments are, at best, unpersuasive and, at worst, disingenuous. The district court noted below that the DSHEA “does not prevent the classification of GBL as a controlled substance analogue,” 286 F.Supp.2d at 952, and the government points out that GBL meets the DSHEA’s definition of a “drug” and is known as a common industrial chemical. In fact Turcotte himself labeled his'shipments of Verve to Internet customers as “cleaning supplies” or “supplies,” not dietary supplements. Id. The DSHEA does not address GBL or BD specifically, so both parties are essentially attempting to shoehorn these substances into the DSHEA’s general definitions. This is a dubious enterprise considering that the CSA addresses the status of GBL explicitly, stating-that it is a “List I chemical” under 21 U.S.C. §§ 802(33) and 802(34). This appears the more relevant provision for our purposes.

Perhaps realizing this, Turcotte next claims that GBL’s status as a “Listed chemical” under the CSA precludes its regulation as a controlled substance. To support this contention, Turcotte points to a DEA regulation which states, in part, that “[ejhemical mixtures containing GBL ... are not subject to regulation.” 65 Fed.Reg. 21,645 (Apr. 24, 2000). But this line of argument is patently without merit. The very regulation cited by Turcotte also explicitly states that the CSA, at 21 U.S.C. § 802(32), expressly provides that “the designation of GBL or any other chemical as a Listed chemical does not preclude a finding that the chemical is a controlled substance analogue and subject to the provisions of 21 U.S.C. 813.” 65 Fed.Reg. 21,645 (Apr. 24, 2000) (citing 21 U.S.C. § 802(32)) (emphasis added). See also Ansaldi, 372 F.3d at 128 n. 6 (also ruling that GBL’s status as a listed chemical under DEA regulations does not preclude its regulation as a controlled substance analogue under the CSA). In fact Turcotte himself concedes that the clear provisions of . the CSA (at 21 U.S.C. § 802(32)(B)) doom his argument, though he tries to blunt the impact of this point by hiding it in a footnote. See Appellant’s Br. at 30 n. 11 (conceding that “GBL’s designation as a listed chemical does not preclude a finding that the chemical is a controlled substance analogue. 21 U.S.C. § 802(32)(B).”).

Having obliterated his own argument regarding GBL’s susceptibility to regulation, Tureotte next argues in the alternative that, even if GBL can be regulated as a controlled substance analogue (as he concedes), the various laws and regulations cited here render GBL’s status confusing, and the rule of lenity should be applied to reverse his conviction. While the rule of lenity instructs that ambiguity in the meaning of a statutory provision should be resolved in favor of the defendant, this principle is only applicable where there is a “grievous ambiguity or uncertainty in the language and structure of the Act.” U.S. v. Ranum, 96 F.3d 1020, 1030 (7th Cir.1996) (quoting United States v. Neal, 46 F.3d 1405, 1410 (7th Cir.1995)) (internal quotations omitted). In other words, the rule of lenity “only serves as an aide for resolving an ambiguity; it is not to be used to beget one.” Callanan v. United States, 364 U.S. 587, 596, 81 S.Ct. 321, 5 L.Ed.2d 312 (1961).

As just discussed, the law is perfectly clear on this point: As per both the CSA itself and the DEA regulation cited by Tureotte, GBL is not exempt from regulation under the CSA as a controlled substance analogue. Tureotte himself acknowledges this fact in his brief. See Appellant’s Br. at 30, n. 11. See also Ansaldi, 372 F.3d at 128 n. 6 (observing that the DEA “regulation [concerning GBL] does not even purport to remove any substance from the realm of criminal conduct.”). The rule of lenity is not applicable here. This is especially so given our rejection of Turcotte’s vagueness claims — it would be passing strange for us to rule that a statute, while not unconstitutionally vague, is sufficiently ambiguous to trigger the rule of lenity.

For all of these reasons, Turcotte’s claim that federal law precludes the regulation of GBL as an analogue of GHB are patently without merit.

2. GHB’s Status as a Controlled Substance

Having attempted to question GBL’s susceptibility to regulation in its own right, Tureotte next claims that GHB was not properly scheduled as a controlled substance, and therefore that GBL cannot be regulated as a controlled substance analogue of GHB. Tureotte asserts that GHB was put on Schedule I at the behest of the Attorney General in March of 2000 as a temporary or emergency scheduling under 21 U.S.C. § 811(h), which expires if not made permanent within one year. Tur-cotte then claims that since GHB’s status as a Schedule I controlled substance allegedly expired in March of 2001, he cannot be convicted for possession or distribution of its analogues, including GBL. The government responds by asserting that Congress directed the Attorney General to place GHB on Schedule I in Public Law 106-172, and thus that the aforementioned time limit applicable to emergency sched-ulings should not apply.

We need not attempt to navigate this legislative thicket because Turcotte’s expiration claim fails for a more basic reason: Even if the scheduling of GHB expired in March of 2001 as Tureotte claims, it is undisputed that GHB was still a Schedule I controlled substance at the time of the conduct leading to Turcotte’s arrest and conviction (the summer of 2000). Matters of timing similarly thwart Turcotte’s claim that FDA approval of Xyrem' — a, drug for treating narcolepsy that contains GHB — in July of 2002 converted GHB to a Schedule III substance not subject to the CSA’s Analogue Provision. Aside from the fact that FDA approval of a specific drug for certain medical uses need not have any bearing on the status of its component chemicals in non-medical contexts, the FDA’s approval of Xyrem came after Turcotte’s misconduct and subsequent arrest in September of 2000. Thus, even if the FDA approval of Xyrem has some effect on the status of GHB as a controlled substance — a proposition which appears extremely dubious to begin with — that approval still would not have any bearing on Turcotte’s conviction.

Turcotte’s claims as to the status and/or scheduling of GHB under the Controlled Substances Act are thus unpersuasive, and we affirm the ruling of the district court on this point.

F. Turcotte’s Sundry Procedural Claims

Finally, in addition to the more fully developed claims examined above, Turcotte tacks on five allegations of trial errors and procedural infirmities. These claims are not discussed in the decision below and presumably were not raised before the district court. They are presented in such a cursory and unelaborated fashion that we feel justified in dismissing them outright. In this circuit, unsupported and undeveloped arguments are waived. See United States v. Toney, 27 F.3d 1245, 1249 (7th Cir.1994); United States v. Berkowitz, 927 F.2d 1376, 1384 (7th Cir.1991); Pelfresne v. Village of Williams Bay, 917 F.2d 1017, 1023 (7th Cir.1990); United States v. Williams, 877 F.2d 516, 519 (7th Cir.1989).

Yet even were we to indulge Turcotte and take these claims seriously, they still fail on their own terms. Turcotte’s claim that “the use of expert testimony regarding GHB was irrelevant to testimony concerning GBL and BD,” is false. Testimony concerning the health effects of GHB was directly relevant to the second and third clauses of § 802(32)(A), which require controlled substance analogues to have similar actual or purported physiological effects to controlled substances. Thus consideration of GHB’s physiological effects was crucial to the jury’s determination that GBL, in light of its own physiological effects, is an analogue of GHB.

Turcotte’s second claim, that his “sentence was necessarily based upon the sale of all three substances [GHB, BD and GBL],” is little more than a weak reprise of assertions made earlier in the brief concerning disjunctive versus conjunctive readings of § 802(32)(A). For the reasons discussed in that portion of our opinion, supra, this claim is directly contradicted by the record and is thus unsupportable.

Turcotte’s third claim alleges that the district court improperly allowed two unqualified witnesses to testify as experts regarding the similarity of effects between GHB, GBL and BD. Even if Turcotte had raised this claim previously — which apparently he did not — we still review for abuse of discretion only. United States v. Van Dreel, 155 F.3d 902, 905 (7th Cir.1998). Given that both witnesses had advanced scientific degrees (one had a Ph.D. in medical anthropology and one was a medical doctor) and both had published extensively on the effects of GHB and GBL, there is no evidence that the district court abused its discretion in certifying them as expert witnesses.

The fourth claim concerns an episode in which a juror in the case encountered a prosecution witness during a court recess and asked the witness for a mint. Turcotte alleges that the court should have made a more extensive inquiry into the incident or granted Turcotte a mistrial. Turcotte presents absolutely no evidence of any wrongdoing or resulting prejudice connected with this ostensibly chance encounter, and thus he has not even begun to carry his burden of demonstrating an abuse of discretion by the district court. See United States v. Cassano, 372 F.3d 868 (7th Cir.2004) (district court’s decision not to grant a mistrial is reviewed for abuse of discretion).

Finally, Turcotte’s allegation of ineffective assistance of counsel is likewise too sparse and unsupported to gain any traction. Turcotte’s unsubstantiated and largely conclusory statements fall far short of carrying his burden of persuasion as to the two elements of the test outlined in Strickland v. Washington, 466 U.S. 668, 689, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). See United States v. Davenport, 986 F.2d 1047, 1049 (7th Cir.1993) (defendant bears burden of proof and persuasion to establish ineffective assistance of counsel). We also note that, should Turcotte wish to pursue his ineffective assistance claim in earnest, such a claim is best brought in a collateral proceeding under 28 U.S.C. § 2255. See Massaro v. United States, 538 U.S. 500, 504, 123 S.Ct. 1690, 155 L.Ed.2d 714 (2003) (Observing that “in most cases a motion brought under § 2255 is preferable to direct appeal for deciding claims of ineffective-assistance”).

Accordingly, we reject four of these five claims, which seem to be added as afterthoughts to Turcotte’s main arguments, and we decline to rule on the fifth (ineffective assistance) at this juncture.

IV. CONCLUSION

For the foregoing reasons, we Affirm the decision of the district court. 
      
      . "GHB” is Gamma Hydroxybutyric Acid, a Schedule I Controlled Substance under federal regulations. Gamma Butyrolacetone ("GBL”) and 1,4-butanediol ("BD”) are substances that convert to GHB in the human body.
     
      
      . The government cites United States v. Hussein, 351 F.3d 9, 17 (1st Cir.2003), United States v. Cain, 130 F.3d 381, 384 (9th Cir.1997), United States v. Barbosa, 271 F.3d 438, 457-58 (3d Cir.2001) and United States v. Fuller, 162 F.3d 256, 260 (4th Cir.1998), for the proposition that convictions under the CSA do not require defendants to know that the substances in question are controlled substances. These citations are quite misleading. Despite the government’s contrary contentions (or insinuations), all of these cases affirm the baseline principle that defendants must know that the substances in their possession are controlled substances to be convicted under the CSA, even if they do not know the exact identity of the substance they possess. In other words, the language cited by the government deals with defendants' legal rather than factual knowledge. Defendants need not know that possession of a controlled substance is illegal, but they still must know that they possess a controlled substance.
      All of these cases also involve traditional, well-known narcotics that are illegal per se, such as cocaine (Cain), heroin and cocaine base (Barbosa) and crack (Fuller).' Thus, once again, knowledge of the drug's identity would be sufficient to establish knowledge of the drug's status as controlled. The Hussein case involves a nontraditional drug called khat, and the Hussein court accordingly recognized the traditional/nontraditional distinction (though not in those terms), requiring the defendant to know both that he possessed khat and that khat in turn contained the controlled substance cathinone. 351 F.3d at 17.
     
      
      . Such a situation might appear to raise vagueness concerns, and the Second Circuit's recent decision in United States v. Ansaldi is instructive on this point. The court begins by noting that *‘[i]t is an interesting question under what circumstances a statute that depends on the resolution of a factual question about which reasonable juries can disagree is specific enough to withstand a vagueness challenge.” 372 F.3d 118, 123 (2d Cir.2004). The court then notes that "[¡Juries are often required to determine not only whether certain conduct occurred but also whether the conduct falls within the definition of a statute,” citing the Supreme Court’s ruling, in considering an obscenity law, that "the possibility that different juries might reach different conclusions as to the same material does not render the statute unconstitutional.” Id. at 123 n. 2 (citing Smith v. United States, 431 U.S. 291, 309, 97 S.Ct. 1756, 52 L.Ed.2d 324 (1977)). Statutes only encounter vagueness difficulties if their terms are "so vague that a jury’s determination is likely to be arbitrary, and, consequently, those terms would not allow an ordinary person to understand what conduct is prohibited.” Id. For more discussion of such issues, see our discussion of the vagueness question, infra.
      
     
      
      
        . As both the Supreme Court and this Court have made clear, this kind of non-mandatory inference does not place any improper evi-dentiary burden on the defendant as long as "there is a ‘rational connection’ between the basic facts that the prosecution proved and the ultimate fact presumed, and the latter is 'more likely than not to flow from' the former." County Court of Ulster County, New York v. Allen, 442 U.S. 140, 165, 99 S.Ct. 2213, 60 L.Ed.2d 777 (1979). The jury is always free to accept or reject any such permissible inference, and it remains the government's burden to prove all the elements of the offense beyond a reasonable doubt. Such carefully circumscribed inferences and presumptions are thus a "staple of our adversary system of factfinding.” Id. at 156, 99 S.Ct. 2213. This is especially so where questions of knowledge or intent are at issue since, as a practical matter, a defendant’s state of mind always "must be determined circumstantially, by inference.” Pigee v. Israel, 670 F.2d 690, 692 (7th Cir.1982). By contrast, mandatory or conclusive presumptions, which require the jury to infer some "ultimate” or "elemental” fact from the existence of "evidentiary” or "basic” facts, present much stickier constitutional problems.' For definitive discussions of inferences, presumptions and the issues surrounding them, see Allen, 442 U.S. at 156-67, 99 S.Ct. 2213; Sandstrom v. Montana, 442 U.S. 510, 514-27, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979); Pigee, 670 F.2d at 692-97.
     
      
      . There is evidence that the website through which Turcotte sold Verve 5.0(GBL) contained assertions that Verve is the "absolute finest quality GHB precursor” and that its ingredients are "illegal nationwide.” For his part, Turcotte attempts to blunt the import of this evidence, claiming that he played no part in building the website and had no knowledge of GBL’s chemical similarities to GHB. While Turcotte’s testimony on this score perhaps seems dubious, we recognize that weighing contradictory evidence and making credibility determinations are functions generally reserved for the jury. Accordingly, on appeal we may not impute the requisite knowledge to Turcotte based on these website assertions, however much they may affect the equities of the situation.
     
      
      . See also our discussion of Turcotte's vagueness claims, infra at section III-D.
     
      
      . We pause to note that the jury also found that Turcotte intended or represented that GBL has similar physiological effects to GHB. Thus, as a matter of common sense, it would seem strange to allow Turcotte to claim he did not know GBL is an analogue of GHB.
     
      
      . The exact language of the Roberts court's analysis reads as follows:
      Given the combination of GHB's cognizable similarity to 1,4-butanediol prior to ingestion and its metabolization into that controlled substance after ingestion, the classification of 1,4-butanediol as a controlled substance analogue is clearly mandated by the Act's language, and remains so regardless of the differences of view among the experts. In short, given the circumstances of this case, an evaluation of the the statute's vagueness as-applied does not call for the fine distinctions drawn by the experts.
      363 F.3d at 127.
     
      
      . The Ansaldi court speaks in no uncertain terms on the vagueness issue:
      Regardless of any other ways in which the laws governing controlled substance[s] might be vague, there is one thing they make perfectly clear — the sale of GBL for human consumption is illegal.
      The subsection defining "controlled substance analogue” specifically states that "[t]he designation of gamma butyrolactone ... as a listed chemical ... does not pre-
        
        elude a finding ... that the chemical is a controlled substance analogue.” 21 U.S.C. § 802(32)(B) (emphasis supplied). Thus, GBL is one of the substances that the statute actually identifies as a potential controlled substance analogue.
      372 F.3d at 122-23.
     
      
      . See also our discussion of these provisions in relation to Turcotte’s scienter claim, supra at section III-B.
     
      
      . See footnote 5, supra.
      
     
      
      . The government argues for a deferential standard of review as to these claims, noting that they were either raised in an untimely filed post-trial motion, United States v. Withers, 972 F.2d 837, 844 (7th Cir.1992) (reviewing such claims for clear error), or raised for the first time on appeal. United States v. Noble, 246 F.3d 946, 955 (7th Cir.2001) (reviewing such claims for clear error). The exact standard of review applicable here is of no consequence, since Turcotte’s claims are doomed even under de novo review.
     
      
      . See discussion of Turcotte's vagueness claim, supra.
      
     
      
      . The district court makes precisely this point in its ruling below, noting that "even if we were to accept defendant’s argument that the scheduling had expired, GHB was clearly listed in Schedule I during the period of time in which defendant was found to have possessed and distributed the substances.” 286 F.Supp.2d at 952.
     