
    UNITED STATES of America, Plaintiff-Appellee, v. Daniel James STANFORD, Defendant-Appellant.
    No. 15-30127.
    United States Court of Appeals, Fifth Circuit.
    May 18, 2016.
    
      Camille Ann Domingue, Asst. U.S. Atty. (argued), U.S. Attorney’s Office, Robert Chase Abendroth, Alexander Coker Van Hook, Esq., Asst. U.S. Atty., Lafayette, LA, for Plaintiff-Appellee.
    Robin Elise Schulberg, Attorney (argued), Covington, LA, Daniel James Stanford, Stanford Law Office, Lafayette, LA, for Defendant-Appellant.
    Before DAVIS, SMITH, and HIGGINSON, Circuit Judges.
   JERRY E. SMITH, Circuit Judge:

Daniel Stanford, one of the defendants in a series of cases involving a synthetic-marihuana distribution ring, appeals, on numerous grounds, his conviction and sentence on charges of conspiracy to distribute and to possess with intent to distribute a controlled substance analogue (“CSA”) (in violation of 21 U.S.C. §§ 846, 841(b)(1)(C), 813, and 802(32)(A)); conspiracy to introduce and cause to be introduced misbranded drugs into interstate commerce (in violation of 18 U.S.C. § 371 and 21 U.S.C. §§ 331, 333(a)(2), and 352(a), (b), and (f)); conspiracy to engage in money laundering (in violation of 18 U.S.C. § 1956(h)); and money laundering (in violation of 18 U.S.C. § 1957). Based on the intervening decision in McFadden v. United States, — U.S. —, 135 S.Ct. 2298, 192 L.Ed.2d 260 (2015), announced after this trial, we reverse the conviction of conspiracy to distribute a CSA because the district court’s error, in ruling that the government was not required to prove that Stanford knew the synthetic marihuana compound distributed by the conspirators was a CSA, was not harmless, despite the decision to send the issue to the jury via a special interrogatory. We affirm the conviction and sentence on all other counts and remand for proceedings as needed.

I.

In 2011, Richard Buswell, the owner of a chain of smoke shops in the Lafayette, Louisiana, area, became involved with a group of persons selling and producing synthetic marihuana, a lab-created product designed to mimic organic marihuana. Manufacturers hoped to skirt drug laws because, at least initially, lawmakers and law enforcement officials were not well informed regarding synthetic eannabi-noids, and the chemicals used to create the products had not yet been universally banned.

Originally, many makers of synthetic marihuana used a chemical known as JWH-018, but as public awareness grew, the federal government announced a ban on JWH-018, forcing producers to switch to a chemical known as AM-2201. Structurally, JWH-018 is similar to AM-2201, except that AM-2201 replaces a hydrogen atom in JWH-018 with a fluorine atom. Both JWH-018 and AM-2201 are na-phthoylindoles that activate the eannabi-noid receptors in the human body, producing a “high.”

Buswell met with Thomas Malone, Drew Green, and Boyd Barrow in March 2011 seeking to stock a synthetic cannabinoid in Buswell’s smoke stores, Curious Goods. Malone and Green owned a Georgia-based company called NutraGenomics that had formulated a line of synthetic marihuana they called “Mr. Miyagi.” Barrow owned Pinnacle Products (“Pinnacle”), a company that distributed Mr. Miyagi to retailers in a number of states. Over time, Pinnacle also began manufacturing Mr. Migayi for NutraGenomics with Joshua Espinoza, a Pinnacle salesman, personally mixing batches. In an effort to skirt the law, Mr. Miyagi was sold as “potpourri,” and its label stated that it was “not for human consumption.” As of March 2011, Pinnacle used only AM-2201 to make Mr. Miyagi.

Shortly thereafter, Mr. Miyagi arrived in Curious Goods’ stores in Lafayette. In July 2011, a Louisiana law went into effect that banned naphthoylindoles. Although Barrow and others were initially concerned, Buswell assured Barrow that there would be no problem selling Mr. Miyagi in Louisiana. To help provide those assurances, Buswell brought in Barry Do-mingue, a local attorney who served as the corporate attorney for Curious Goods.

That summer, Barrow traveled to Lafayette and met with Buswell and Domingue, who told him that they had talked with law enforcement regarding Mr. Miyagi, and there would be no issues. Further, Barrow testified that about a week after his trip to Lafayette, Buswell called and told him that he had hired a “constitutional lawyer,” Stanford, “who would lead our fight into ... challenging the feds and challenging states with the ultimate goal of regulation.”

Stanford had first become connected with Buswell by serving as his defense counsel in a securities-fraud prosecution. After Buswell’s call, Barrow flew to Lafayette to meet with Stanford and Buswell. Buswell instructed him to tell Stanford “everything about the business,” and Barrow complied, describing Mr. Miyagi, how it was manufactured, and how it was labeled (specifically the “not for human consumption” warning). Stanford even opened and smelled a package of Mr. Mi-yagi. Barrow claimed that the meeting lasted one-and-a-half to two hours.

Barrow testified that at some point after that meeting, he received a call from Bus-well saying that Stanford was onboard— they had “the big stick.” Buswell also claimed that Stanford had secured an agreement with the Louisiana attorney general that Mr. Miyagi was the only “potpourri” that could be “sold in the state” and that Buswell had a letter to that effect from the attorney general’s office.

The first physically documented interaction Stanford had with the drug scheme occurred on August 22, 2011, when he received an email from Daniel Francis. Francis, who had a personal penchant for cannabinoids, had formed — at the suggestion of Malone and Green — a political action committee for the synthetic marihuana industry — the Coalition for Cognitive Liberty — to lobby and recommend manufacturing guidelines. Similarly, working with manufacturers such as NutraGenom-ics, Francis formed the Retail Compliance Association (“RCA”), incorporated under California law, to keep retailers abreast of the latest regulatory developments and to track legislation affecting cannabinoids.

Francis’s email was entitled “RCA membership related documents” and contained nothing but attachments related to the RCA, including documents describing the organization, guidelines for how to display synthetic marihuana products, and advice on interactions with police. Francis claimed the email was a follow-up to an introductory phone call he had with Stanford, although Stanford contends that his phone records show no evidence of such a call. On August 26, Francis sent a followup email asking whether Stanford had “received the documents.” Francis also mentioned a possible misunderstanding “on the call” and provided clarification that the RCA was “available as a plaintiff.” The same day, Stanford replied that he “did receive the documents” and was “currently reviewing” them and would contact Francis “sometime next week.”

Espinoza testified that he went to Lafayette in August (“either the second or third week”) and met with Buswell, Do-mingue, Barrow, and Stanford at a restaurant. Domingue was introduced as “Curious Goods’ attorney,” Stanford as Buswell’s “corporate attorney.” Do-mingue told Espinoza, who still had concerns about the legality of Mr. Miyagi in Louisiana, that they had gotten the product “approved by the AG ... the District Attorney ... all the local authorities.” Stanford and Domingue were sitting on either side of Buswell, yet Stanford said nothing in regard to Domingue’s statement about approval from the authorities.

Francis testified that he traveled to Lafayette in September. He gave a presentation at a meeting at Buswell’s house, where he went through his “standard spiel” for attorneys, covering “the cannabi-noid receptor, why these products work, why they’re on the market, why they’re being sold,” as well as the “Analogue Act.” Present were Barrow, Buswell, Espinoza, Stanford, and Domingue; nevertheless, other witnesses testified that “Stanford showed up later” and “came in at the end of the meeting.”

Francis described the meeting “as a dynamic conversation,” not just a solo presentation. He covered “the exact chemical that was being used in this, which was AM-2201” and its relation to the DEA ban. Francis claimed he “tried to represent it in a way that was legal.” He also stated that they “didn’t feel threatened by the Analogue Act,” because they “didn’t think the science [presumably,' demonstrating the similarity of AM-2201 to JWH-018] existed at the time.” Nevertheless, Francis talked about how AM-2201 and JWH-028 were “visually similar.” Francis testified that he told Stanford specifically about the industry’s shift from JWH-018 to AM-2201. The group “handled,” “displayed,” and “opened” a package of Mr. Miyagi at the meeting. Barrow and Buswell suggested forming a Louisiana branch of the RCA.

Barrow testified that at some time in October, he and Espinoza traveled to Lafayette with the primary purpose of getting Buswell, Domingue, and Stanford to show them the purported letter from the attorney general. After Buswell declined to talk about the letter over dinner, Barrow showed up at Stanford’s law office and demanded to see it. Stanford confessed that there was no letter but insisted he had “a gentleman’s handshake agreement” with the attorney general allowing them to sell Mr. Miyagi in the state.

On October 27, Domingue forwarded Stanford an email that purported to have, as attachments, lab reports on Mr. Miyagi, although the reports were not actually attached. Domingue specifically noted the presence of AM-2201. On November 2, Francis emailed Stanford several documents for a meeting that day, including a budget and business plan for the RCA. On November 3, at Barrow’s request, Stanford emailed a reporter a response to a story about a teenage boy who had died after smoking synthetic marihuana.

Stanford and Francis continued to communicate throughout November about forming a Louisiana RCA. On November 8, Stanford sent Francis an email asking to discuss “orginizing [sic] the RCA into a real powerhouse and discuss what it would take to make you a full time executive director.” The same day, Don Wirt-shafter, a lawyer who specialized in can-nabinoids, told Francis that AM-2201 was included in Louisiana’s ban of naphthoy-lindoles. Francis testified that, before the call with Wirtshafter, he had not been aware that AM-2201 was covered by the Louisiana law. Francis decided to tell Stanford about that development in person and claimed that he did so on his next trip to Lafayette (although he provided no date). He told Stanford, who reassured him that he (Stanford) would have lunch with the attorney general.

Around the middle of November, one of the Curious Goods franchisees had a run-in with law enforcement after an off-duty state trooper noticed a sign out front promoting Mr. Miyagi. Stanford then met with the store’s owner, along with Do-mingue, Francis, and Buswell, at his law office. The owner testified that either Francis or Domingue told him that Mr. Miyagi had been sent to the “DEA’s own lab” and found not to contain “any banned substances.” On the table at the meeting was a lab report that said “DEA Registered Analytical Laboratory” at the top.

Stanford followed up with the trooper via phone on November 22. Francis testified that Stanford told the trooper that the products were legal and offered samples to prove it, although he never actually did so. According to Francis, that conversation occurred after Francis had told Stanford about the Louisiana ban on AM-2201. In late November, the chief of police testified that he also met with Stanford, who told him that “everything that was inside the store was DEA cleared.” Stanford agreed to produce a sample of Mr. Miyagi to the police lab for testing, though he never did.

On November 28, the Louisiana-based RCA was incorporated in Louisiana with Stanford as “Director” and Francis as “President.” Barrow explained that he and Buswell agreed that Pinnacle and Curious Goods would pay for the initial costs of getting the Louisiana RCA up and running; they settled on paying Stanford a combined total of $12,500 a week. Rather than splitting those costs each week, sometimes Barrow, and at other times Buswell, made a “bulk payment.” The following chart summarizes payments to Stanford.

On December 7, Buswell, Stanford, Do-mingue, Francis, Espinoza, and Barrows — all of whom were involved with Curious Goods — met at Buswell’s house. One of the purposes was to educate Curious Goods employees and franchisees on selling Mr. Miyagi and how to handle law-enforcement inquiries. According to Francis, Barrow, and Espinoza, various topics were discussed, including accounting, warehouse distribution, merchandising, and how to use the cash-register system. Buswell announced that all franchisees would have to pay the RCA weekly dues of $1000 to $5000. Membership in the RCA was mandatory, and Stanford would serve as its head. Francis testified that he, in addition to Stanford, spoke on behalf of the RCA. Stanford was introduced as the “big stick” and again claimed to have an agreement with the attorney general. At the end of his presentation, Stanford allegedly admonished, “remember, nobody talks, everybody walks” and then left.

On December 8, local narcotics agents raided Curious Goods stores, executing warrants and seizing Mr. Miyagi, computers, and other items. Buswell was arrested the same day, and Stanford initially served as his counsel until he was disqualified in light of mounting evidence against himself. Meanwhile at least some of the conspirators and franchisees wanted to keep doing business with a different product that had not yet been banned. Barrow testified that Stanford met with them and formulated new operational guidelines. Those plans never went anywhere, however, and the distribution scheme came to an end.

II.

In September 2012, Stanford was charged in a joint indictment with Green, Malone, Barrow, Espinoza, Buswell, Francis, Domingue, and others as follows: Count One: conspiracy to distribute and to possess with intent to distribute a Schedule I controlled dangerous substance (in violation of 21 U.S.C. §§ 846, 841(b)(1)(C), 813, and 802(32)(A)); Count Two: conspiracy to introduce and cause to be introduced misbranded drugs into interstate commerce (in violation of 18 U.S.C. § 371 and 21 U.S.C. §§ 331, 333(a)(2), and 352(a), (b), and (f)); Count Three: money-laundering conspiracy (in violation of 18 U.S.C. § 1956(h)); Counts Four through Thirteen: money laundering (in violation of 18 U.S.C. § 1957). Trial began in March 2014 for Stanford and Domingue after other defendants had pled out. After Do-mingue committed suicide the third day of trial, the district court granted Stanford’s motion for a mistrial.

A new trial for Stanford began in August 2014. Before both trials, in light of a circuit split, Stanford contended that for the government to prove him guilty of conspiracy to distribute or possess with intent to distribute a controlled substance (Count One), it must demonstrate that he knew AM-2201 was a CSA. The district court rejected that theory, concluding that the Fifth Circuit did not require such knowledge and that it was enough to show that Stanford knew the substance was AM-2201 and that AM-2201 was in fact a CSA. Nevertheless, to preserve the issue, the court ruled that Stanford could put on evidence regarding his lack of knowledge that AM-2201 was a CSA, and the court determined to send the issue to the jury via a special interrogatory.

Stanford represented himself but chose not to testify. After ten days, the jury returned a guilty verdict on Counts One, Two, Three, Four, Five, Ten, Eleven, and Thirteen and not-guilty verdicts on the remaining counts. It also answered “yes” to the special interrogatory regarding Stanford’s knowledge that AM-2201 was a CSA. Stanford unsuccessfully moved for a new trial, asserting, among other claims Brady, Jencks Act, and Napue violations.

The district court held an evidentiary sentencing hearing in December and sentenced Stanford in January 2015. The court determined that the adjusted offense level on the drug group (Count One) was 30, and the adjusted offense level on the money-laundering group (Count Three) was 32, and it selected the higher offense level as the overall basis as required by U.S. Sentencing Guidelines (“U.S.S.G.”) § 3D1.3(b). The advisory range for that offense level was 121-151 months. The court rejected Stanford’s request for a below-guidelines sentence and chose the low end of the advisory range — 121 months for Counts One and Three. The court also sentenced Stanford to 60 months on Counts Two, Four, Five, Ten, Eleven, and Thirteen, to be served concurrently with the other sentence. The sentence included six years of supervised release on Count One and three years on the other counts.

III.

Stanford contends that the district court erred by determining that knowledge that AM-2201 was a CSA was not a required element under Count One. In McFadden, 135 S.Ct. at 2303-05, the Court held that to be convicted under the Analogue Act, 21 U.S.C. § 813, and the Controlled Substances Act, 21 U.S.C. § 841(a)(1), which the Analogue Act incorporates by reference, “the Government must prove that a defendant knew that the substance with which he was dealing” was a CSA. Thus, jury instructions that fail to incorporate that element of knowledge are error, subject to harmlessness analysis. McFadden, 135 S.Ct. at 2307.

McFadden was decided while this case was on appeal. Stanford claims that because the district court similarly failed to instruct the jury regarding knowledge in relation to Count One — conspiracy to distribute and possess with intent to distribute a CSA — it erred, and the error was not harmless. Stanford also contends that as a result of the court’s determination that such knowledge was not a required element, he was denied the opportunity to present a complete defense. In turn, the government concedes that the court’s ruling about proof of knowledge and its failure to instruct the jury on that element were likely error but maintains that any error was harmless. We conclude that the error was not harmless.

A.

In regard to Count One, the district court instructed the jury that it must be convinced that the government had proved the following elements beyond a reasonable doubt:

First, that two or more persons, directly or indirectly, reached an agreement to distribute and/or possess with the intent to distribute a particular substance; Second, that the defendant knew what the substance was, in this case AM-2201;
Third, that AM-2201 was a [CSA]; Fourth, that the defendant knew the substance was intended for human consumption;
Fifth, that the defendant knew of the unlawful purpose of the agreement;
Sixth, that the defendant joined in the agreement willfully, that is, with the intent to further its unlawful purpose.

After instructing the jury on all the elements for the thirteen counts, the court added “one last question,” which it told the jury was “unrelated to [its] answers to the other charges in the indictment.” The court explained that “[t]his question is separate and apart from the other questions listed above on the jury verdict form.” The “sole purpose,” of the “last question is to assist the Court,” and the jury’s answer “must be unanimous just as it is on the other questions on the verdict form.” The question was, “During the [relevant] time period ... do you find that the defendant, Daniel James Stanford, knew that AM-2201 was a controlled substance analogue?”

Notably, before listing the elements for each count, the court explained that the government would have to prove each element “beyond a reasonable doubt.” During its explanation of the final special interrogatory, however, the court did not mention the standard of proof or direct that the government was required to prove anything at all in this regard.

1.

Although we typically review jury instructions for abuse of discretion, when the objection is based on statutory interpretation, review is de novo. See United States v. Garcia-Gonzalez, 714 F.3d 306, 312 (5th Cir.2013) (quoting United States v. Wright, 634 F.3d 770, 774 (5th Cir.2011)). “Generally, failure to instruct the jury on every essential element of the offense is error.” United States v. Williams, 985 F.2d 749, 755 (5th Cir.1993).

2.

As the government acknowledges, under McFadden, the failure to instruct on knowledge in Count One was error. The critical issue is whether it was harmless. “Erroneous jury instructions are harmless if a court, ‘after a “thorough examination of the record,” is able to “conclude beyond a reasonable doubt that the jury verdict would have been the same absent the error.” ’ ”

The government contends that the special interrogatory made the error harmless. Initially, that theory appears strong. In a similar case, United States v. Dvorak, 617 F.3d 1017, 1026 (8th Cir.2010), the court concluded that the presence of a special interrogatory made the failure to instruct on a required element harmless. Dvorak involved identity theft. At the time of trial, proof that the defendant knew he was stealing the identities of real people was not a required element under circuit law; after trial, the Supreme Court ruled that it was required. Much like the district court a quo, the court in that case recognized that the issue might later be contested and thus submitted the question of knowledge via a special interrogatory. Id. at 1025-26.

The Eighth Circuit said that was enough to alleviate any error, reasoning that “there [wa]s no need to guess as to whether a rational jury would have found Dvorak guilty if the proper instructions were given because a rational jury did find that he met the additional element of the statute — that is, that he knew the means of identification belonged to another person.” Id. at 1026. Likewise, the government here contends that because the jury made a finding on the missing element of knowledge, any error in failing to include it as one of the elements of Count One was harmless.

There are notable differences between this case and Dvorak First, there is nothing to indicate that the court in Dvorak told the jury that the special interrogatory was only “to assist the Court.” By culling the interrogatory in this manner, the district court here indicated to the jury that the special interrogatory did not require the same level of attention as did the various counts of the indictment.

a.

More significantly, in Dvorak, the court instructed the jury on the burden of proof for the special interrogatory — it had to find “beyond a reasonable doubt” that the defendant had knowledge. Id. at 1025. Here, the court gave no instruction on the burden of proof for the interrogatory. Stanford points to this circuit’s pattern jury instructions, which note that when special interrogatories are used to establish additional fact issues, the jury should be asked what “was proved beyond a reasonable doubt.” The pattern instructions state generally that the jury “must be convinced that the government has proved each of the following [elements] beyond a reasonable doubt” and then include the special interrogatory as one of the elements for the crime at issue. In other words, the burden of proof precedes the list of elements, and any special interrogatories directly follow that list, appearing to the jury as another element. The district court employed that format (burden of proof followed by the elements) for each of the thirteen counts but not in regard to the interrogatory (neither treating it as its own count nor making it appear as an additional element under Count One).

Thus, Stanford reasons that, because the court separated the special interrogatory from Count One, as well as from all of the other counts, and told the jury it was “separate and apart” from the other issues, the jury could not have known what standard of proof to employ. In response, the government points to various other places in the instructions where the court said that the government had the burden of proof beyond a reasonable doubt.

For example, before delving into any of the specific counts, the court told the jury that “it is your job to decide whether the government has proved the guilt of the defendant beyond a reasonable doubt.” Indeed, the court mentioned the reasonable-doubt standard at least eight times in the overview portion of the instructions, apart from its recitation of the burden of proof before each count. The government claims that because it was the only standard of proof mentioned, the jury must have known to apply the reasonable-doubt standard to the special interrogatory. Therefore, to decide the overall issue of whether the interrogatory made the failure to instruct the jury on knowledge harmless, we must determine whether the failure to specify the burden of proof for the interrogatory was itself harmless.

i.

A threshold question is whether harmless-error analysis applies at all where the district court does not state the burden of proof. Under McFadden, 135 S.Ct. at 2307, there is little doubt that failure to instruct on the element of knowledge is subject to review for harmlessness and does not require automatic reversal. There the Court remanded for consideration of harmless error. There is, however, no case directly on point for how to review failure to provide the standard of proof for a special interrogatory.

In Sullivan v. Louisiana, 508 U.S. 275, 277, 113 S.Ct. 2078, 124 L.Ed.2d 182 (1993), the trial judge gave the wrong definition of reasonable doubt (nearly identical to another jury instruction that had been held unconstitutional), and the Court held that it was error, not subject to harmless-error analysis. Id. at 277-81, 113 S.Ct. 2078. Without the proper standard of proof, there was “no jury verdict of guilty-beyond-a-reasonable-doubt,” making “the question whether the same verdict of guilty-beyond-a-reasonable-doubt would have been rendered absent the constitutional error ... utterly meaningless.” Id. at 280, 113 S.Ct. 2078.

The inquiry, in other words, is not whether, in a trial that occurred without the error, a guilty verdict would surely have been rendered, but whether the guilty verdict actually rendered in this trial was surely unattributable to the error. That must be so, because to hypothesize a guilty verdict that was never in fact rendered — no matter how inescapable the findings to support that verdict might be — would violate the jury-trial guarantee.

Id. at 279, 113 S.Ct. 2078. Here, one could reach a similar conclusion' — -because the jury was not given a standard of proof for the special interrogatory, it issued no actual verdict on the knowledge question; thus, there is no jury determination to review for harmlessness.

Nevertheless, in Neder v. United States, 527 U.S. 1, 15, 19-20, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999), the Court held that where a court failed to instruct on an entire element of the crime, the error was subject to harmlessness analysis, and the Court in fact found it harmless. The trial court had erroneously decided not to submit the issue of materiality to the jury as one of the elements of filing a false tax return; instead the court determined that it was an issue for the judge, not the jury. Id. at 6, 119 S.Ct. 1827. Concluding that such a mistake did not require automatic reversal, the Court distinguished “structural” errors, which are “subject to automatic reversal,” from the “traditional harmless-error inquiry.” Id. at 8, 14, 119 S.Ct. 1827. Structural errors are limited to a narrow class of cases that “infect the entire trial process,” necessarily rendering “a trial fundamentally unfair.” Id. at 8, 119 S.Ct. 1827 (quoting Brecht v. Abrahamson, 507 U.S. 619, 630, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993); Rose v. Clark, 478 U.S. 570, 577, 106 S.Ct. 3101, 92 L.Ed.2d 460 (1986)). In contrast, typical harmless-error inquiries involve errors with far more limited effects.

The Neder Court observed that !<[i]t would not be illogical to extend the reasoning of Sullivan from a defective ‘reasonable doubt’ instruction to a failure to instruct on an element of the crime.” Id. at 15, 119 S.Ct. 1827. Nevertheless, the Court noted other cases in which the jury was instructed on the wrong legal test (or not instructed at all), yet the Court had found the error subject to harmlessness analysis. Considering that precedent, as well as the fact that reversal would send the case back for retrial on other contested issues, while the defendant had not contested the evidence of materiality, the Court concluded that the failure to instruct on materiality also was subject to harmless-error analysis. Id. Therefore, at least in Neder, the Court rejected the formal, categorical approach in favor of a functional, case-by-case determination regarding whether an instruction error can be considered harmless.

Thus, on one side, Sullivan holds that an instruction stating the wrong standard of proof can never be harmless, and, on the other, Neder holds that omitting an entire element is subject to harmless-error analysis. In the wake of Sullivan, it may be tempting to place all errors regarding the standard of proof in the same box — automatic reversal — but that is hard to reconcile with Neder. Notably, Sullivan involved an instruction stating the wrong standard of proof; that is different from providing no standard at all, or stating the correct standard but discussing it only in relation to other charges.

Omission of the standard of proof appears closer to the omission of an entire element in Neder than to instruction on the wrong standard in Sullivan. We can assume that in Sullivan the jury must have applied the wrong standard, because the only instruction on the burden of proof was erroneous; here, however, it is certainly possible that the jury applied the correct standard — it was properly instructed on beyond-a-reasonable-doubt in the overview portion of the instructions. Additionally, though Neder did not overrule Sullivan, the Court retreated from a formalistic approach to questions of error in jury instructions, following the case-by-case determination of harmlessness that it had applied previously. All of these considerations lead us to conclude that omission of the standard of proof in a special interrogatory is subject to harmless-error analysis.

ii.

Neder is instructive on whether omission of the standard of review is harmless. The Court explained that “no jury could reasonably find that Neder’s failure to report substantial amounts of income on his tax returns was not ‘a material matter.’ ” Id. at 16, 119 S.Ct. 1827. If the missing income was not material, there was no reason for Neder to exclude it from his tax returns. Therefore, “[t]he failure to report such substantial income incontrovertibly established] that Neder’s false statements were material to a determination of his income tax liability.” Id. Indeed, the “evidence supporting materiality was so overwhelming, in fact, that Neder did not argue to the jury — and d[id] not argue [before the Court] — that his false statements of income could be found immaterial.” Id. In sum, the missing element was logically encompassed by a guilty verdict and was not in fact contested.

Similarly, in Dvorak, 617 F.3d at 1026, the court, when considering whether the failure to instruct the jury on knowledge was harmless, observed, in addition to its analysis on the special interrogatory, that it would have been impossible for the defendant to conduct his identity-theft scheme without knowledge that he was stealing the identities of real children — the “scheme could only work if the children actually existed.” Thus, a finding of knowledge was logically implicit in the guilty verdict on identity theft. Therefore, in both Neder and Dvorak the error was considered harmless where proof of the element missing from the instruction was inherent in proof of the overall conviction, so the jury could not have failed to find the element.

Here, on the other hand, the missing standard of proof was not intrinsically linked to the answer to the special interrogatory. The jury could have found that Stanford knew AM-2201 was a CSA, with or without assurance beyond a reasonable doubt. It may very well be that the jury imported the reasonable-doubt standard into the interrogatory, given the fact that the court mentioned that standard multiple times in its overview of the case. Yet, it is also entirely plausible that, after finding Stanford guilty, the jury hastily answered the extra question without considering any degree of certainty, because it was told that the interrogatory was only for the benefit of the court and was “separate and apart” from the indictment.

Without a recital of the burden of proof, we, in addition to being unaware of the level of certainty for the jury’s determination that Stanford had knowledge, also do not know whether the jury thought the government had met the burden to prove such knowledge. Before listing the elements for each of the counts, the court told the jury that it must be convinced that the government had proved guilt beyond a reasonable doubt. For the special interrogatory, the court merely asked the jury to determine whether Stanford “knew that AM-2201 was a controlled substance analogue.” The government’s burden of proof was not mentioned at all (presumably because the court had ruled that the government did not need to prove knowledge). It is one thing to think that Stanford had knowledge (regardless of what has been proved) and another to decide that the government actually has demonstrated such knowledge.

These uncertainties indicate that the failure to specify the burden of proof was not harmless. The cases cited by the government do not counsel the opposite holding. To support its claim that omitting the reasonable-doubt standard was harmless, the government points to a decision that the failure to include the “beyond a reasonable doubt” language in one portion of the jury instruction was harmless where “the trial judge advised the jury at seven different points in the instructions that they must find the defendant guilty beyond a reasonable doubt.” United States v. Brown, 522 F.2d 10, 11 (9th Cir.1975) (per curiam). Nevertheless, in Brown, the omission of the burden of proof did not occur in relation to a specific count or element of a crime but, instead, in a preamble to the instruction to be careful of bias or prejudice that “might affect a juror’s verdict.” Id. at 12. The court had used the “beyond a reasonable doubt” phrase in “its instruction on the presumption of innocence,” “its instructions on the quantum of proof necessary for a verdict of guilty,” “in stating the burden of the Government to prove ‘every essential element’ of the crime charged,” “in stating the rule for finding guilt by circumstantial evidence,” and, perhaps most importantly, before its charge “on proof of the elements.” Id. at 11-12. Additionally, because the defendant had failed to object to the instruction at trial, the court’s review was only for plain error. Id. at 11. Brown involved no special interrogatory and is easily distinguishable.

The government also cites Gorin v. United States, 313 F.2d 641, 654 (1st Cir.1963), for the proposition that when only one standard is given, we should presume that the jury applied it to all questions. There the court vacated a conviction where the only burden of proof mentioned in the jury instructions was “beyond a reasonable doubt,” yet the defendant’s actual burden for a certain defense was only a “preponderance of the evidence.” Id. That decision surely does not establish that the instant district court’s failure to specify the burden of proof in relation to the special interrogatory was harmless. If anything, one could claim under Gorin that failure to specify a standard of proof in relation to a specific issue is not harmless. The government cites no other cases to support its position.

We ordinarily presume that jurors “follow the instructions they are given.” Yates, 500 U.S. at 403, 111 S.Ct. 1884 (citing Richardson v. Marsh, 481 U.S. 200, 211, 107 S.Ct. 1702, 95 L.Ed.2d 176 (1987)). Conversely, absent an appropriate instruction, we cannot presume that the jurors applied the correct standard of proof. Yet, a defendant is “indisputably entitled” to “a jury determination that [he] is guilty of every element of the crime with which he is charged, beyond a reasonable doubt.” Where, as here, the court gives a separate, special interrogatory, instructs the jurors that it is only for the benefit of the court, and does not recite the burden of proof before the interrogatory (but does recite the burden of proof before each of the actual counts), we cannot conclude beyond a reasonable doubt that the jury applied the reasonable-doubt standard to the interrogatory. The error was not harmless.

b.

This case differs from Dvorak and Neder in another respect. As discussed, in both of those cases a finding on the missing element was inherent in the other elements that the jury actually found. In contrast to the knowledge at issue in Dvorak or the materiality at issue in Neder, here a finding that Stanford knew that AM-2201 was a CSA was riot logically inherent in proof of Count One. Indeed, concluding that he knew that his co-conspirators were distributing AM-2201 and that AM-2201 is in fact a CSA is different from finding that he knew that AM-2201 was a CSA. That is especially true given the conspirators’ attempts to stay one step ahead of the law by selling drugs that had not yet been scientifically proven to be similar to marihuana or JWH-018.

Although the government posits that the issue was actually before the jury in the form of the special interrogatory (and putting aside any concerns about the burden of proof), that is not the end of the relevant analysis. The jury was merely asked whether Stanford “knew that AM-2201 was a controlled substance analogue?” There was no instruction on what knowledge meant or how proof of knowledge could be demonstrated. '

In McFadden, the Court outlined two ways to prove knowledge that a substance is a CSA. First, knowledge “can be established by evidence that a defendant knew that the substance with which he was dealing is some controlled substance — that is, one actually listed on the federal drug schedules or treated as such by operation of the Analogue Act — regardless of whether he knew the particular identity of the substance.” McFadden, 135 S.Ct. at 2305. In other words, if a defendant “know[s] that the white powder [he is distributing] is listed on the schedules even if he does not know precisely what substance it is,” he is “guilty of knowingly distributing ‘a controlled substance.’ ” Id. at 2304. Because there is little doubt that Stanford knew that the conspiracy was dealing AM-2201, this method of proof appears inapt.

The second method, of proof of knowledge “can be established by evidence that the defendant knew the specific analogue he was dealing with, even if he did not know its legal status as an analogue.” Id. at 2305.

The Analogue Act defines a controlled substance analogue by its features, as a substance “the chemical structure of which is substantially similar to the chemical structure of a controlled substance in schedule I or II”; “which has a stimulant, depressant, or hallucinogenic effect on the central nervous system that is substantially similar to or greater than” the effect of a controlled substance in schedule I or II; or which is represented or intended to have that effect with respect to a particular person.

Id. (quoting 21 U.S.C. § 802(32)(A)). Thus, “[a] defendant who possesses a substance with knowledge of those features knows all of the facts that make his conduct illegal....” Id. He “need not know of the existence of the Analogue Act to know that he was dealing with ‘a controlled substance.’ ” Id. In other words, if Stanford knew that AM-2201 was substantially similar to JWH-018 in its chemical structure and produced a substantially similar “high,” he had the requisite knowledge that AM-2201 was a CSA. There is little doubt that this is a significantly greater burden of proof than just demonstrating that he knew the conspirators were distributing AM-2201 and that AM-2201 was in fact a CSA.

Yet at the time of trial, the Supreme Court’s explication on the two ways to prove knowledge had not yet been announced, so the jury was not instructed on those tests. Though it is theoretically possible that the jury divined the se,cond method of proof based on the instruction in Count One on how to determine whether AM-2201 was a CSA (it had to have both a similar chemical structure and similar stimulant effect to JWH-018), that is a significant presumption, especially given that the interrogatory was discussed at the end of the instructions,- with twelve other counts between it and Count One.

The government claims that there was, nonetheless, ample proof that Stanford knew AM-2201 was a CSA, pointing to evidence that he was present for discussions of the similarity of AM-2201 to JWH-018 both structurally and in its physical effects on users. Yet, it is one thing for the government to look back now that the Court has provided the proper framework and pick out evidence that fits into that framework; it is another to assume that the jury focused on the same evidence, without the benefit of that framework, when it answered the special interrogatory. We do not know whether, in answering it, the jury credited the testimony to which the government directs us.

Therefore, because the jury was not aware of the Supreme Court’s test for proof of knowledge, the special interrogatory did not render harmless the failure to instruct on proof of knowledge, even apart from the missing specification of the burden of proof. The attempt to avoid retrial by submitting the special interrogatory was laudable but ultimately unsuccessful.

B.

Stanford maintains that the district court’s determination that knowledge was not a required element under Count One prevented him from presenting a complete defense. Without unambiguously identifying a constitutional source, the Supreme Court has repeatedly recognized that the “Constitution guarantees criminal defendants ‘a meaningful opportunity to present a complete defense.’ ” “The right to present a complete defense under the Sixth Amendment ‘is an essential attribute of the adversary system.’ ” Violations of a right to present a complete defense “are reviewed for harmless error.”

1.

Because they focus on a missing element, Neder and Dvorak are the decisions most on point, despite that they are focused on harmlessness from the perspective of a jury’s not being instructed on an element rather than on a defendant’s being unable to make a complete defense. Cases involving a claim that the defendant was denied the right to present an adequate defense typically involve the court’s excluding certain testimony or evidence rather than a contention that the defendant would have changed his trial strategy if he had known a particular element was required.

As we have noted, to evaluate harmlessness, the courts in Neder and Dvorak asked whether proof of the missing element was an inherent part of the proof at trial. See supra part III.A.2.a.ii. Thus, in Neder, 527 U.S. at 16-17, 119 S.Ct. 1827, the Court noted that evidence of materiality was logically inherent in Neder’s failure to report his actual income. Indeed, the government’s evidence of materiality was so significant that Neder did not even try to dispute it. Id. at 16, 119 S.Ct. 1827. And in Dvorak, 617 F.3d at 1026, the court noted that evidence of the missing element of knowledge that the defendant was stealing the identities of real people was inherent in the overall proof regarding the identity-theft scheme. Applying the reasoning of those cases, the critical question is whether proof rebutting the missing element of knowledge was inherent in Stanford’s defense of other elements.

The government misses the point in focusing only on the evidence actually presented at trial. Cobbling together evidence that the prosecution offered for other issues to demonstrate that Stanford likely had the requisite knowledge ignores the possibility that he might have done more to counter that evidence if he had known that it mattered for the verdict. As we have said, proof that he knew that AM-2201 was a CSA is quite different from proof that he knew his coconspira-tors were selling AM-2201 and proof that it is in fact a CSA.

Assuming arguendo that the government presented sufficient evidence of knowledge to convict, if Stanford was not on notice that he needed to combat such proof, we cannot conclude that he had the chance to present a complete defense. Just as the jury did not know of the two methods for proof of knowledge outlined in McFadden, Stanford also was oblivious of them. Without awareness of the relevant legal standards, he could not have determined the best way to defend against proof of knowledge.

Stanford contends that if he had known that knowledge was a required element of the conspiracy charge, he “would have focused his defense on that element because it was the weak link in the government’s case.” Specifically, he claims that he would have called a forensic chemist, Lindsay Reinhold, to testify that in “late 2011 there were no generally accepted scientific criteria for determining whether a substance satisfied the statutory definition of a controlled substance analogue.” Instead, Stanford argues that the “court’s ruling that knowledge was not an element of the drug conspiracy required [him] to adopt a different trial strategy.”

The government, citing United States v. Clements, 73 F.3d 1330, 1336 (5th Cir.1996), responds that absent a proffer of truth at trial, there is no way to assess the “potential admissibility, value, and effectiveness” of this testimony. The government is correct that we cannot determine the potential added value of Reinhold’s testimony. Without further information, we do not know whether it would have been admissible, and if it was, we do not know whether the jury would have credited it. See, e.g., Apprendi, 530 U.S. at 490, 120 S.Ct. 2348.

The fact that we cannot assess the potential value of this evidence does not mean that Stanford should be denied the opportunity to present it. It could be that Reinhold’s testimony would have been ex-cludable or unhelpful; indeed, if Stanford were retried and given the opportunity to present Reinhold’s testimony, it might make no difference to the outcome. But we should not prejudge a defendant’s trial strategy. The error is not harmless unless proof of the missing element was inherent in proof of one of the others.

There is a further wrinkle. The district court ruled that knowledge was not required, but before trial it also informed Stanford that it would send this issue to the jury via a special interrogatory. The court said it would allow him “to put on evidence” regarding his “lack of knowledge that AM-2201 was a controlled substance analogue.” Thus, Stanford was not without notice that the issue would go to the jury, and in theory he was given the opportunity to rebut evidence of such knowledge.

In fact, the government claims that Stanford did attempt to establish a defense to knowledge that AM-2201 was a CSA, for example, “by cross examining the government’s expert chemists and other witnesses on the difficulty a layperson might have in discerning the similarities between two chemical compounds.” According to the government, Stanford “made good use of any favorable testimony on these points.”. Indeed, in his closing statement, he claimed he was unaware AM-2201 was illegal.

Thus, if Stanford was on notice that the issue would be going to the jury, and did in fact attempt to defend himself from a finding of knowledge, it is harder to conclude that he was denied the ability to make a complete defense. We are left with his claim that he would have structured his defense differently if he were aware that knowledge was a required element. That is not an unreasonable assertion. Even though Stanford was aware that the jury would be ruling on whether he knew AM-2201 was a CSA, if the government did not have to prove such knowledge to convict him, it makes sense that Stanford would expend less energy on this issue. Additionally, as discussed, he could not have been aware of the two Supreme Court-sanctioned methods for proving such knowledge, so he lacked the notice needed to prepare an appropriate defense. It follows that the error was not harmless.

IV.

Stanford maintains that a new trial is called for because the government solicited (or failed to correct) false testimony in violation of Napue v. Illinois, 360 U.S. 264, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959). We review an order denying a new trial for abuse of discretion. United States v. Wall, 389 F.3d 457, 465 (5th Cir.2004). “This standard is necessarily deferential to the trial court because we have only read the record, and have not seen the impact of the witnesses on the jury or observed the demeanor of the witnesses ourselves, as has the trial judge.” United States v. O’Keefe, 128 F.3d 885, 893 (5th Cir.1997). Where there are mixed questions of law and fact, as in Napue-based claims, we review “the underlying facts for abuse of discretion, but the conclusions to be drawn from those facts de novo.” Wall, 389 F.3d at 465.

“[A] new trial based upon a Napue violation is proper only if (1) the statements in question are shown to be actually false; (2) the prosecution knew that they were false; and (3) the statements were material.” O’Keefe, 128 F.3d at 893. Even assuming that the prosecution presented (or failed to correct) false testimony, the critical factor is materiality. “It is axiomatic that not every lie is material.” Id. at 894. The Supreme Court has “defined materiality in terms of a ‘reasonable probability’ of a different outcome,” id. (quoting Kyles v. Whitley, 514 U.S. 419, 434, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995)), which “results when nondisclosure places the case in a different light so as to undermine confidence in the verdict,” id. This is determined by examining “the challenged evidence collectively, not on an item-by-item basis.” Id. “To say that an error did not contribute to the verdict is, rather, to find that error unimportant in relation to everything else the jury considered on the issue in question, as revealed by the record.” Id. (quoting Yates, 500 U.S. at 403, 111 S.Ct. 1884).

Stanford claims that there were three main presentations of false testimony. First, he posits that Francis lied by testifying to phone conversations he had with Stanford between September and November 2011. Stanford points to records from his cell phone, subpoenaed by the government, that do not show any calls to him from Francis’s cell phone or landline until November 8. That theory, however, overlooks the possibility that Francis called Stanford from another phone — at a hotel, or perhaps on a burner phone. Additionally, Francis’s emails to Stanford in August 2011 imply that they spoke via the phone; one dated August 26 specifically mentions a “call.” Yet even if no call occurred, Francis’s emails to Stanford make it obvious that he was communicating with Stanford as early as August, which undermines Stanford’s contention that he did not become involved in the conspiracy until later. Thus, Stanford’s claim about the phone records — even if true — does not rise to the level of materiality.

Next, Stanford maintains that the prosecution solicited false testimony from Francis implying that Stanford was listed on the agenda to present about the RCA at the December 7 meeting. That agenda showed “Dan” as discussing the RCA, and both Francis and Stanford have a first name of Daniel. Francis testified that he presented on the RCA, and Stanford also spoke “on behalf of’ the RCA at the meeting. The prosecutor immediately followed up: “Okay. So here you have an explanation in this as Dan generically in the RCA. Regardless of who that is, is that an accurate reflection of the RCA’s presentation and who was going to participate?” Francis agreed: “Yes.”

That testimony, which did not definitively state that “Dan” referred to Stanford, hardly ■ seems false. Stanford does not deny that he spoke, and it was his discussion of the RCA at the meeting that mattered for purposes of assessing his involvement with the conspiracy, regardless of whether he was originally scheduled to speak. The testimony is not material.

The most objectionable testimony regarding the agenda came during Stanford’s cross-examination of Espinoza, who testified that “Dan” on the agenda referred both to Dan Francis and Dan Stanford. Yet, “when the defense elicits the alleged perjury on cross-examination, no material falsehood has occurred because the government has not itself knowingly presented false testimony.” O’Keefe, 128 F.3d at 894. If Espinoza’s testimony was wrong, as Stanford contends, it was Stanford’s duty to correct him. There were no material falsehoods regarding the agenda.

Stanford avers that payments made to him “were falsely represented as RCA dues.” He claims that the government elicited false testimony that checks made out to him by Buswell and Barrow that had “RCA dues,” “retainer,” and “legal services” written in the memo line were in fact RCA dues. Stanford’s claim regarding the checks that had “RCA dues” written on them does not pass the straight-face test. Similarly, Stanford presents scant evidence that checks with the memo lines of “retainer” or “legal services” were for something other than his RCA work.

As an example, Stanford points to a check of $12,500 written by Barrow on October 28, 2011, noting “retainer” in the memo line. Barrow testified that the check was “to get the RCA off and funded.” Yet, Stanford contends that his own business records indicate he was hired by Barrow “out of concern that his association with Buswell, then under indictment for securities fraud, might draw law enforcement scrutiny on him.” Even if Barrow was lying about the reason for that check, there was enough other evidence connecting Stanford to the conspiracy financially — the checks that explicitly said “RCA dues.”

Even if some of the checks for legal fees were not related to the RCA, at least two (for $16,250 and $19,000) included the words “RCA dues,” linking Stanford to the conspiracy. Stanford tries to come up with an alternate explanation for one of those checks, pointing to alleged inconsistencies in testimony about the check. Yet, considering the plain language— “RCA dues” — the jury was entitled to draw its own conclusions about the purpose. Any inconsistencies in testimony are not material. In sum, although the falsehoods that Stanford alleges are based on apparent evidentiary inconsistencies, it is questionable whether one could describe the inconsistencies as false, let alone material.

Stanford posits that the government erred by evaluating each piece of evidence individually and contends that we should follow the Ninth Circuit and consider the materiality of Napue violations cumulatively. Those decisions are not binding on this circuit, but even if we were to analyze Stanford’s Napue claims cumulatively, combining the alleged falsehoods does not amount to a violation, because the whole is the sum of the parts. As the district court observed, “[t]he alleged peripheral inconsistencies upon which the Defendant focuses ... were immaterial to the trial’s outcome.” Stanford’s Napue claims have no merit.

V.

Stanford says that the government failed to disclose Brady material. Though we generally review the denial of a motion for a new trial for abuse of discretion, we “consider alleged Brady violations de novo.” Turner, 674 F.3d at 428. Brady requires the government to disclose any exculpatory material in its possession. “When a defendant seeks a new trial on the basis of withheld information, he must show that: ‘(1) the prosecution did not disclose the evidence; (2) the evidence was favorable to the defense; and (3) the evidence was material.’ ” United States v. Barraza, 655 F.3d 375, 380 (5th Cir.2011) (quoting United States v. Davis, 609 F.3d 663, 696 (5th Cir.2010)). “Favorable evidence” is evidence that “is exculpatory or impeaching,” but evidence is material only “if there is a reasonable probability that the result of the proceeding would have differed had the prosecution disclosed the evidence.” Id.

Stanford urges us to adopt the approach of three other circuits and hold that a defendant need only be able to raise “a colorable claim” that the undisclosed material contained favorable evidence. Stanford implies that the government should have disclosed any notes from its interviews with witnesses, reasoning that “[i]t seems too plain for argument that rough notes from any witness interview could prove to be Brady material.” Yet, putting aside that the “colorable claim” standard is not the law in this circuit, Stanford misreads the cases from other courts. In the same breath that it quoted the color-able-claim standard, the court in Williams-Davis stated that it was “unwise to infer the existence of Brady material based upon speculation alone.” Williams- Davis, 90 F.3d at 514 (quoting Ramos, 27 F.3d at 71). Indeed, the court went hold to hold that the Brady claim -was meritless because it was based on “bare speculation.” Id. Likewise, in Ramos, 27 F.3d at 71, the court rejected, on the basis of “mere possibility,” the claim that destroyed notes of witness interviews “might have included Brady material.”

Similarly, Stanford’s argument is pure conjecture. He contends that the government’s case shifted over time — focusing on him only after other conspirators had become cooperating witnesses — and he surmises that this must mean that the witnesses’ stories changed. According to Stanford, “the sheer number of times the prosecution interviewed the cooperating co-defendants suggests that the disclosures either changed or grew.” Next, Stanford claims that the government must have made notes or reports of these witness interviews, which must have contained exculpatory material, requiring the government to disclose them.

Stanford has no evidence to support any of these allegations. It is hardly surprising that the government’s case grew as it further investigated the conspiracy. The fact of multiple interviews of witnesses (which hardly seems abnormal in a case as complicated as this) does not mean that the witnesses were changing their stories. Indeed, the more likely explanation is that, as the government built its case, it had new questions for the co-conspirators. Thus, Stanford’s conjectures cannot rise to the level of even a “colorable claim” of Brady material.

Similarly, Stanford’s notions about the- existence of reports or notes from the witness interviews are also speculative. Although the government may have notes from its witness interviews (and the government implicitly acknowledged that at oral argument), Stanford has not pointed to particular documents that he believes contain Brady material. Nor does he appear to have requested in camera review of specific documents for Brady purposes. “[RJeliance on the government’s assurance that it is not in possession of any Brady material may be sufficient when the defense makes a blanket request for favorable material in the government files.” United States v. Diaz-Munoz, 632 F.2d 1330, 1334 (5th Cir. Unit B 1980). Stanford’s Brady argument is unavailing.

VI.

Stanford contends that even if they are insufficient to constitute error individually, cumulatively the government’s failures to provide Brady material and correct falsehoods in violation of Na-pue amount to reversible error. “We have repeatedly emphasized that the cumulative error doctrine necessitates reversal only in rare instances and have previously stated en banc that ‘the possibility of cumulative error is often acknowledged but practically never found persuasive.’ ” United States v. Delgado, 672 F.3d 320, 344 (5th Cir.2012) (en banc) (quoting Derden v. McNeel, 978 F.2d 1453, 1456 (5th Cir.1992) (en banc)). More importantly, “non-errors have no weight in a cumulative error analysis.” Id. Because we have rejected Stanford’s .claims of error under both Na-pue and Brady, together they cannot constitute cumulative error. “[T]here is nothing to accumulate.” Id.

VIL

Stanford claims that the district court erred in sentencing by (1) equating AM-2201 to THC; (2) employing a 1:167 ratio to equate AM-2201 to marihuana; (3) using a starting date of August 22 for Stanford’s participation in the conspiracy; (4) changing the method for calculating the base offense level for money laundering; (5) adding two levels to the base offense level for money laundering; and (6) not giving a two-level credit for a minor role. There is no error.

We employ a two-step process to review a sentence. “First, we must ‘ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, [or] failing to consider the § 3553(a) factors.’ ” “Second, if the sentence is proeedurally sound or if the procedural error is harmless, this Court ‘consider^] the substantive reasonableness of the sentence imposed.’ ” Both steps use an abuse-of-discretion standard under which “[w]e review the district court’s legal interpretation of the Sentencing Guidelines de novo and factual findings for clear error.” “A factual finding is clearly erroneous only if, based on the entirety of the evidence, the reviewing court is left .with the definite and firm conviction that a mistake has been made.” Brooks, 681 F.3d at 712. “A factual finding is not clearly erroneous if it is plausible in light of the entire record.” Id. If an objection is “not properly preserved, we review only for plain error.” Alaniz, 726 F.3d at 618.

A.

Stanford assigns error to the district court’s equation of AM-2201 to synthetic tetrahydrocannabinol (“THC”). Generally, U.S.S.G. § 2D1.1 supplies the offense levels for controlled-substance violations by relying on 21 U.S.C. § 841(b)(1) for -the sentences and equivalency levels. See U.S.S.G. § 2D1.1, application note 8(A), Nevertheless, because § 841(b)(1) only “provides direction for the more common controlled substances,” where a substance is not listed in the ■ statute, the application notes say to identify the base offense level using the following method:

(i) Use the Drug Equivalency Tables to convert the quantity of the controlled substance involved in the offense to its equivalent quantity of marihuana.
(ii) Find the equivalent quantity of marihuana in the Drug Quantity Table.
(iii) Use the offense level that corresponds to the equivalent quantity of marihuana as the base offense level for the controlled substance involved in the offense.

U.S.S.G. § 2D1.1, application note 8(A). If, however, a controlled substance is listed in neither the Drug Equivalency Table nor the Drug Quantity Table, the court is to “determine the base offense level using the marihuana equivalency of the most closely related controlled substance referenced in this guideline.” U.S.S.G. § 2D1.1, application note 6.

JWH-018, the controlled substance for which AM-2201 is an analogue, does not appear in the tables. The district court therefore had to determine which controlled substance listed in the tables was closest to JWH-018. The court decided that the closest was THC, which Stanford claims was error. But as he recognizes, that was the issue in United States v. Malone, 809 F.3d 251 (5th Cir.2015). Indeed, Stanford adopted the portion of Malone’s brief dealing with that issue. In Malone, we upheld the determination that THC was the closest controlled substance to JWH-018 and thus to AM-2201. Id. at 256-58. Malone forecloses Stanford’s claim.

B.

Stanford contends that the district court erred by applying a 1:167 ratio to JWH-018 and, by extension, to AM-2201. That ratio was a direct result of finding that THC is the closest controlled substance to JWH-018 listed in the guidelines. The Drug Equivalency Tables list 1 gram of THC as equal to 167 grams of marihuana. See U.S.S.G. § 2D1.1, application note 8(D).

1.

We make the same decision here as in Malone. Stanford points to testimony from Dr. Nicholas Cozzi contending that there is no scientific basis for the 1:167 ratio. Yet, that testimony is actually from Malone’s trial, so we are foreclosed from reevaluating it under our rule of orderliness. Notwithstanding expert testimony “that the 1:167 ratio has no scientific basis, this Court has squarely held that district courts are not required to engage in ‘a piece-by-piece analysis of the empirical grounding behind each part of the sentencing guidelines’ and ignore those parts that do not pass empirical muster.” Malone, 809 F.3d at 258 (quoting United States v. Duarte, 569 F.3d 528, 530 (5th Cir.2009)). Stanford’s second allegation of sentencing error also is foreclosed.

2.

In a related argument, Stanford contends that the district court erred by failing to recognize its authority, conferred by Kimbrough v. United States, 552 U.S. 85, 128 S.Ct. 558, 169 L.Ed.2d 481 (2007), to vary from the 1:167 ratio for converting THC to marihuana. We also considered Kimbrough in Malone, 809 F.3d at 258-60, and determined that it was “unclear whether the district court properly understood its discretion under Kimbrough”-, nevertheless, we held that any error was harmless. The same statement from the district court regarding its authority to deviate from the guidelines calculation that we found ambiguous in Malone is at issue here, because the defendants in the conspiracy had a joint hearing on the matter. Thus, in regard to the ambiguity of the statement, we are bound by Malone.

As in Malone, any error was harmless. In United States v. Groce, 784 F.3d 291 (5th Cir.2015), we explained that “[a]n erroneous guidelines range calculation is harmless if ‘(1) [ ] the district court would have imposed the same sentence had it not made the error,- and (2)[ ] it would have done so for the same reasons it gave at the prior sentencing.’ ” Id. at 296 (quoting United States v. Ibarra-Luna, 628 F.3d 712, 714 (5th Cir.2010)). “To satisfy these requirements, there must be ‘evidence in the record that will convince [this court] that the district court had a particular sentence in mind and would have imposed it, notwithstanding the error.’ ” Id. (quoting Ibarra-Luna, 628 F.3d at 718). It is the government that has the “heavy burden” of “convincingly demons-trat[ing] that the sentencing court actually would have followed the very same reasoning absent the error.” Robinson, 741 F.3d at 603 (quoting Ibarra-Luna, 628 F.3d at 717).

In Malone, 809 F.3d at 260, we recognized this “heavy burden” and held that idle government had met it because “there [wa]s nothing in the record to indicate that the district court was inclined to vary from the 1:167 ratio or pronounce a lesser sentence.” Instead, “the district court repeatedly commented on the ‘seriousness of the offense’ and declined to accept the extent of the Government’s recommended § 5K1.1 departures.” Id.

There is even more support for harmlessness here. In contrast to an absence of statements indicating that the district court was likely to impose a lower sentence, the court provided affirmative evidence that it had a particular sentence in mind. The court stated that it had given “great thought” to the defendant’s request “to give a variance” from the calculated guideline range of 121 to 151 months. It noted that it had “carefully examined the 3553(a) factors, including the nature and characteristics of the offense ... and the characteristics of the defendant.” Nevertheless, “[b]ecause of the numerous convictions,” it did “not believe that the guideline range, as calculated by the Court, overstate^] Mr. Stanford’s culpability in this matter.” Indeed, it was “troubled by Mr. Stanford’s lack of remorse” and thus concluded that “a guideline sentence [was] justified.” All of this indicates that the court would have imposed the same sentence notwithstanding any Kimbrough error.

Despite its finding of harmlessness, the panel in Malone remanded “for the limited purpose of clarifying the district court’s understanding of its discretion under Kim-brough and, if appropriate, its willingness to deviate from the advisory range on such grounds.” Malone, No. 14-31426, Order Granting Limited Remand, Doc. No. 119 (Feb. 2, 2016). Because there is a stronger basis for concluding here that any Kim-brough error would not have changed the overall sentence, we decline to remand. The government has met its “heavy” burden by showing, from the record, that the district court had a particular sentence in mind.

C.

Stanford assigns error to the district court’s identification of August 22 as the beginning of his involvement in the conspiracy; Stanford says it should be November 1. His theory is that based on bank and phone records, the alleged meetings that various witnesses testified occurred between and among Stanford, Barrow, and Espinoza could not have happened until mid-September at the earliest. Even if they occurred in August, as the government contends, Stanford claims that his knowledge of the conspiracy was limited and that there was insufficient evidence that he knew then of the scheme’s criminal nature. He maintains that November 1 is appropriate because that was three days after Barrow had written the check for the alleged RCA dues and two days before Stanford’s meeting with Francis, which resulted in his letter to a television reporter on behalf of the “yet-to-be formed Louisiana RCA.”

There is no error. The court based its August 22 date on the first email from Francis to Stanford. Francis testified that the email was a follow-up to a telephone call with Stanford, although Stanford claims that the phone records indicate that that never happened. That email, which contained only attachments related to the RCA, suggests that Francis had spoken to Stanford, given that it seems improbable that he would send, to someone to whom he had never spoken, a blank email with attachments. The follow-up email Francis sent on August 26 specifically refers to a possible misunderstanding “on the call,” providing strong evidence that a call actually had occurred. Thus, there is good reason to suppose that Francis and Stanford were talking on the phone by late August. Yet, even without any phone calls, Francis’s emails to Stanford indicate that they were communicating during that time.

Although the scope of Stanford’s knowledge in August is uncertain, at a minimum, given the documents Francis emailed to-him, Stanford must have known that the RCA was attempting to skirt the law (one such document is a guide to “Police Interaction,” while another discussed avoiding product names “that insinuate[ ] a relationship to natural cannabis”). Dating Stanford’s involvement in the conspiracy to his first-documented interaction with Francis regarding the RCA does not rise to clear error if it is error at all.

D.

Stanford contends that the district court erred by changing the method for calculating the base offense level for money laundering at the sentencing hearing. The guidelines outline two ways to calculate the base offense level for money laundering:

(1) The offense level for the underlying offense from which the laundered funds were derived, if (A) the defendant committed the underlying offense (or would be accountable for the underlying offense under subsection (a)(1)(A) of § 1B1.3 (Relevant Conduct)); and (B) the offense level for that offense can be determined; or
(2) 8 plus the number of offense levels from the table in § 2B1.1 (Theft, Property Destruction, and Fraud) corresponding to the value of the laundered funds, otherwise.

U.S.S.G. § 2Sl.l(a). The presentence report (“PSR”) used the second method. Nevertheless, at the sentencing hearing the prosecutor contended that the first method was the appropriate one, and the court agreed. Although Stanford does not dispute that the court’s method was correct, he claims that its decision to switch from the second method to the first at the hearing deprived him of the right to notice under Federal Rule of Criminal Procedure 82(i)(l)(C) and U.S.S.G. § 6A1.3, which require that parties are given a chance to comment on disputed factors.'

“[T]he touchstone of [R]ule 32 is reasonable notice to allow counsel adequately to prepare a meaningful response and engage in adversary testing at sentencing.” The notice requirement applies to facts underlying the sentencing determination, not to legal rules the district court employs. Indeed, it is “[fjactual matters not included in the presentence report” that should “be disclosed in advance of sentencing so that the government and the defendant are able to contest inaccuracies.” Thus, when evaluating notice in Garcia, 797 F.3d at 323, we discussed the defendant’s “actual knowledge of the facts on which the district court base[d] an enhancement or a denial of a reduction.”

In contrast, “if the defendant has actual knowledge of the facts on which the district court bases an enhancement or a denial of a reduction, the Sentencing Guidelines themselves provide notice of the grounds relevant to the proceeding sufficient to satisfy the requirements of Rule 32 and U.S.S.G. § 6A1.3.” United States v. Knight, 76 F.3d 86, 88 (5th Cir.1996); see also Garcia, 797 F.3d at 323. “We do not believe that the Guidelines themselves are too complicated, or that the average defense counsel is insufficiently skilled, to render adequate preparation unduly difficult without specific notice of all grounds for an enhancement or for a denial of a reduction.” Knight, 76 F.3d at 88.

Stanford knew all of the underlying facts that led the court to apply the first method of calculation under Section 2Sl.l(a). He therefore had sufficient notice that that method of calculating his base offense level might be more appropriate than the method recommended in the PSR. Notably, in regard to the base offense level for money-laundering, the PSR stated that the “guideline for 18 U.S.C. § 1956(h) offenses is found in USSG § 2S1.1 of the guidelines.” Though it went on to discuss the application of Section 2Sl.l(a)(2), a careful look at Section 2S1.1 could have indicated to Stanford that calculation under Section 2Sl.l(a)(l) was also a possibility.

Additionally, even if the court had erred by denying him notice, Stanford cannot demonstrate that such an error would have affected his “substantial rights.” Fed. R.CRIM.P. 52(a). Because Stanford was a part of the conspiracy that produced the laundered funds, Section 2Sl.l(a)(l), not (a)(2), was the proper method. On appeal, Stanford does not claim otherwise or indicate how he would have objected to the decision if he had notice of the possibility of sentencing under (a)(1). The application of (a)(1) did not violate Stanford’s right to notice, and even if it had, any error was harmless.

E.

Stanford contends that the district court erred by adding a two-level enhancement under U.S.S.G. § 2Sl.l(b)(2)(B), which says to increase the base offense level by two levels “[i]f the defendant was convicted under 18 U.S.C. § 1956.” Stanford avers that there was insufficient evidence to show a conviction under § 1956.

Because Stanford did not preserve an objection, our review is only for plain error. See Alaniz, 726 F.3d at 618. “We find plain error when (1) there was an error or defect; (2) the legal error was clear or obvious, rather than subject to reasonable dispute; and (3) the error affected the defendant’s substantial rights.” United States v. Juarez, 626 F.3d 246, 254 (5th Cir.2010). When considering the sufficiency of the evidence, we are “highly deferential” and “view the facts in the light most favorable to the verdict.” United States v. Kuhrt, 788 F.3d 403, 413 (5th Cir.2015) (quoting United States v. Moreno-Gonzalez, 662 F.3d 369, 372 (5th Cir.2011)). The critical question “is whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Id. (quoting Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979)).

Stanford contends that there was insufficient evidence to support a conspiracy to violate 18 U.S.C. § 1956(a)(l)(A)(i). At issue is Count Three, which charged Stanford with conspiring to engage in money-laundering in violation of both 18 U.S.C. § 1956(a)(1)(A)(i) and 18 U.S.C. § 1957(a). The conspiracy itself was a violation of 18 U.S.C. § 1956(h), which provides that “Any person who conspires to commit any offense defined in this section or section 1957 shall be subject to the same penalties as those prescribed for the offense the commission of which was the object of the conspiracy.” Because § 1956(h) ties the penalty for its violation to the penalty for the crime that is the object of the conspiracy, the question is whether the evidence was sufficient for conviction of a conspiracy to violate § 1956(a)(l)(A)(i). The penalty for a violation of § 1956(a) is greater than for § 1957(a). Compare 18 U.S.C. § 1956(a)(1) with 18 U.S.C. § 1957(b)(1). Similarly, U.S.S.G. § 281.1(b)(2)(B) directs a two-level enhancement for convictions under § 1956, while U.S.S.G. § 2Sl.l(b)(2)(A) instructs only a one-level enhancement for convictions under § 1957.

“To sustain a conviction under the money laundering promotion statute [18 U.S.C. § 1956(a)(1)(A)© ], the Government must show that the defendant: (1) conducted or attempted to conduct a financial transaction, (2) which the defendant then knew involved the proceeds of unlawful activity, (3) with the intent to promote or further unlawful activity.” Stanford disputes the application of the third element, whether he had the requisite “intent to promote or further unlawful activity.”

To satisfy the intent requirement, “the government must show the transaction at issue was conducted with the intent to promote the carrying on of a specified unlawful activity.” United States v. Trejo, 610 F.3d 308, 314 (5th Cir.2010) (citing United States v. Brown, 186 F.3d 661, 670 (5th Cir.1999)). “It is not enough to show that a money launderer’s actions resulted in promoting the carrying on of specified unlawful activity.” Id. Instead, the “the evidence must show that the defendant’s conduct not only promoted a specified unlawful activity but that he engaged in it with the intent to further the progress of that activity.” Id.

Where the underlying unlawful activity is drug distribution, “courts have often relied on proof that the defendant was aware of the inner workings of and/or extensively involved in the drug organization responsible for the criminal activity as circumstantial proof that he had the specific intent to promote its unlawful purpose.” Id. at 315. Indeed, “in the context of a sufficiency challenge to a money-laundering conspiracy ... direct evidence ‘is unnecessary; each element may be inferred from circumstantial evidence.’ ” Cessa, 785 F.3d at 174 (quoting United States v. Fuchs, 467 F.3d 889, 906 (5th Cir.2006)). Stanford contends that he could not have had the specific intent to promote the conspiracy because he used the payments received from Buswell and Barrow for legitimate personal expenditures. According to Stanford, “[t]here was no evidence that he fnnneled the payments back into the distribution of Mr. Miyagi, as did most of his co-defendants.”

Stanford’s argument focuses on what he did after he received the payments, not the transactions by which he received payment in the first place. The statute does not require that one receive proceeds from illicit activity and-then funnel them back into the activity; it merely requires that one conduct (or attempt to conduct) “a financial transaction which in fact involves the proceeds of specified unlawful activity ... with the intent to promote the carrying on of specified unlawful activity.” § 1956(a)(l)(A)(i). In other words, if the transaction by which one' receives illicit funds is made with the intent to promote unlawful activity, the statute can be violated. Thus, by being paid to help further the Mr. Miyagi scheme with proceeds from the sales of Mr. Miyagi, Stanford engaged in promotional money laundering. It does not matter how he spent the tainted funds after receiving them.

This is not a novel interpretation of the statute. We have evaluated money-laundering cases in which a person was allegedly hired to provide services to a criminal ring and paid with illicit proceeds. For example, in Cessa, 785 F.3d at 173-75, a defendant was convicted of “concealment money laundering.” Concealment money laundering, which violates § 1956(a)(1)(B)®, is identical to promotional money laundering, which violates § 1956(a)(1)(A)®, except that concealment money laundering requires' knowledge “that the transaction’s design was to conceal or disguise the nature or source of the illegal proceeds,” while promotional money laundering requires an “intent to promote or further illegal actions.” Cessa, 785 F.3d at 174 n. 6. Both concealment and promotional money-laundering require a “financial transaction,” which “involves the proceeds of specified unlawful activity.” § 1956(a)(1).

Cessa involved the question whether a defendant, who provided horse-training services to a horse-race fixing, narcotics-trafficking conspiracy, had committed concealment money laundering when he was paid with illicit funds. Cessa, 785 F.3d at 175. We concluded that there was insufficient evidence that the defendant had “joined the conspiracy knowing the conspiracy’s purpose was to conceal drug money.” Id. at 179. He was merely a horse trainer and not “aware of the inner workings of [the] criminal narcotics-trafficking organization.” Id. Nevertheless, we did not rule out the possibility that someone with the requisite level of knowledge (or specific intent) who was hired to provide services to a criminal organization and paid in proceeds from its criminal operations could be found to have engaged in money laundering.

Although “merely providing services to a known drug dealer and accepting the proceeds of the illegal activity as payment is insufficient as a matter of law to establish criminal liability for money laundering,” one who engages in all of the above and voluntarily joins the conspiracy “knowing its purpose and with the intent to further the illegal purpose” may be convicted of money laundering. Id. (quoting Fuchs, 467 F.3d at 906). The critical issue is whether Stanford “was aware of the inner workings” of the conspiracy “or extensively involved” in it. Trejo, 610 F.3d at 315. Under our highly deferential review of the facts underlying the conviction, there is plenty of evidence to support an affirmative answer to both questions.

Stanford was paid with illicit funds not merely to provide traditional legal services to the conspirators, but also to assist the Mr. Miyagi scheme in crucial ways. For example, Stanford promoted the falsehood regarding the attorney general, sent information to the local press about Mr. Miyagi, and handled police interactions with the conspirators. As the December 7 meeting indicates, Stanford was an integral player who helped sell the distribution scheme to franchisees. There appears little doubt that he was both aware of the inner workings of the drug conspiracy and extensively involved in it.

Thus, Stanford meets all three elements of a conspiracy to violate § 1956(a)(1)(A)® — he engaged in a financial transaction (he was hired by the conspirators) that he knew involved illicit proceeds (sales of Mr. Miyagi) with the specific intent of furthering the drug scheme (by providing integral support to the conspiracy). See Brown, 553 F.3d at 782. There was sufficient evidence to support the conviction of a conspiracy to violate § 1956(a)(1)(A)®, and the two-level enhancement was not error.

F.

Stanford asserts that the district court erred by not giving him a two-level minor-role reduction in the offense level for money-laundering conspiracy under U.S.S.G. § 3B1.2. Stanford’s theory is convoluted, but he seems to be claiming that once the offense level for money laundering was based on the underlying offense from which the laundered funds were derived — drug distribution — then his sentence was also based on laundering the total proceeds. Apparently, Stanford believes this was the rationale for the decision to deny the reduction. In reality, Stanford claims that he was only a minor participant in the money-laundering scheme.

Yet, there is nothing to indicate that the district court held Stanford responsible for laundering all of the funds from the drug-distribution scheme. Instead, the court found that he was responsible for laundering only $143,000 and explicitly declined to hold him liable for laundering the full $4,202,332 derived from drug proceeds. Additionally, the court specifically referred to the application notes to U.S.S.G. § 2S1.1, which explain that the decision to grant a reduction under § 3B 1.2(b) remains tied to the actual laundering of funds, not “the underlying offense from which the laundered funds were derived.” U.S.S.G. § 2S1.1, application note 2(C). Thus, the court understood that the propriety of a Section 3B1.2(b) reduction should be based on the money Stanford actually laundered, not the total drug proceeds. Stanford points to nothing in the record indicating otherwise, making his claim without merit.

The fact that Stanford received a minor-role reduction for the drug distribution offense does not mean that he automatically should have received a minor-role reduction for the money-laundering offense. Although, as the district court found, Stanford was responsible for laundering only $143,000, he was also fully responsible for laundering all of these funds — he was directly involved in all of the transactions totaling $143,000. He might have looked like a minor participant if all of the money-laundering transactions totaling $4,202,332, were considered. But because the district court specifically determined that for sentencing purposes it could look only to the $143,000, no one could say he was a minor participant in the laundering of those funds. “[W]hen a sentence is based on an activity in which a defendant was actually involved, § 3B1.2 does not require a reduction in the base offense level even though the defendant’s activity in a larger conspiracy may have been minor or minimal.” United States v. Atanda, 60 F.3d 196, 199 (5th Cir.1995) (per curiam) (citations omitted).

The judgment of conviction and sentence is REVERSED on Count One, AFFIRMED on all other counts, and REMANDED for any other proceedings as needed. 
      
      . Other witnesses indicated the meeting may have been later, maybe at the end of October. Barrow testified that he brought Francis to Louisiana after his confrontation with Stanford regarding the claimed arrangement with the attorney general agreement. Espinoza testified that Barrow’s confrontation with Stanford took place in October.
     
      
      . Stanford disputes that these payments were all for the RCA. See infra part IV.
     
      
      . United States v. Cessa, 785 F.3d 165, 186 (5th Cir.2015) (quoting United States v. Skilling, 638 F.3d 480, 482 (5th Cir.2011)).
     
      
      . The court observed that ''[c]ommon sense also supports this outcome.” Dvorak, 617 F.3d at 1026. The scheme could work only if Dvorak knew he was stealing the identities of real children. Id. See infra part III.A.2.a.ii.
     
      
      . Fifth Circuit Pattern Jury Instructions (Criminal Cases) §§ 2.93, 2.95, 2.98 advisory notes (2015) (stating, in the context of controlled-substance convictions, that courts can employ "a special interrogatory asking the jury to indicate the total amount of the controlled substance it believes was proved beyond a reasonable doubt”); see also United States v. Arnold, 416 F.3d 349, 356 (5th Cir.2005) (approving the use of special interrogatories).
     
      
      . See, e.g., Fifth Circuit Pattern Jury Instructions (Criminal Cases) § 2.93.
     
      
      . The verdict form itself did not list any burden of proof — this was contained only in the jury instructions.
     
      
      . The government claims that Stanford never objected to the language of the special interrogatory but only to its placement. Yet, by objecting to the exclusion of the scienter requirement from Count One, Stanford preserved the beyond-a-reasonable-doubt issue; there was no need for the interrogatory to state the burden of proof if it was one of the elements in Count One. Additionally, Stanford requested that the interrogatory be placed immediately below Count One, and he specifically proposed that the instruction include the “beyond a reasonable doubt” language.
     
      
      
        .Neder, 527 U.S. at 11-12, 15, 119 S.Ct. 1827 (citing Pope v. Illinois, 481 U.S. 497, 499-503, 107 S.Ct. 1918, 95 L.Ed.2d 439 (1987) (holding that error in instructing on the wrong First Amendment standard for obscenity was subject to harmless-error analysis); California v. Roy, 519 U.S. 2, 5, 117 S.Ct. 337, 136 L.Ed.2d 266 (1996) (per curiam) (holding that an instruction for conviction of first degree murder that failed to inform the jury that it must find that the defendant had the “intent or purpose” of aiding the confederate’s crime was subject to harmless-error analysis); Carella v. California, 491 U.S. 263, 264, 266, 109 S.Ct. 2419, 105 L.Ed.2d 218 (1989) (per cu-riam) (holding that an instruction containing an unconstitutional conclusive presumption was subject to harmless-error analysis)). See also Rose v. Clark, 478 U.S. 570, 576-77, 579-80, 106 S.Ct. 3101, 92 L.Ed.2d 460 (1986) (holding that an unconstitutional instruction regarding malice in a murder case was subject to harmless-error analysis).
     
      
      . Cf. Yates v. Evatt, 500 U.S. 391, 403, 111 S.Ct. 1884, 114 L.Ed.2d 432 (1991) (explaining that when a "trial court has instructed a jury to apply an unconstitutional presumption, a reviewing court can hardly infer that the jurors failed to consider it”), disapproved of on other grounds by Estelle v. McGuire, 502 U.S. 62, 72 n. 4, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991).
     
      
      . Before Neder, we also had conflicting decisions regarding whether failure to instruct on an element of the crime was subject to harmless-error analysis. See United States v. Oreira, 29 F.3d 185, 189 n. 6 (5th Cir.1994) (collecting cases). Yet, foreshadowing Neder, in Oreira we employed a harmless-error analysis. Id.
      
     
      
      . Nevertheless, the Court was careful to avoid saying that the jury actually made a finding on materiality, merely stating, instead, that no jury could have reached the opposite conclusion. Justice Stevens contended that the verdict “necessarily included” a determination on materiality. Neder, 527 U.S. at 27, 119 S.Ct. 1827 (Stevens, J. concurring). In response, the majority explained that that was "incorrect” because "the [district] court explicitly directed the jury not to consider the materiality of any false statements.” Id. at 16 n. 1, 119 S.Ct. 1827. Nonetheless, even if the jury made no actual finding, the best reading of the opinion is that the verdict was "the functional equivalent” of a materiality finding, given that there was no reason for the defendant to exclude the missing income from his tax returns if it was not material. Id. at 26, 119 S.Ct. 1827 (Stevens, J. concurring).
     
      
      . Indeed, one could aver (as the government does) that the multiple mentions of the standard of proof in the overview portion of the instructions means that the jury almost certainly applied the reasonable-doubt standard to the special interrogatory. If the court had merely provided that standard in the overview and had not repeated it before each count, this would be a persuasive presumption. Instead, the repetition of the standard before each count is contrasted with its notable absence before the interrogatory.
     
      
      . The erroneous instruction read,
      If you find that the law has not been violated as charged, you should not hesitate for any reason to return a verdict of not guilty. If, however, you find that the law has been violated as charged, you shouldn’t hesitate for any reason to return a verdict of guilty because of some emotional problem like one of sympathy or bias or prejudice.
      
        Brown, 522 F.2d at 11. "Beyond a reasonable doubt” should have been included after "find” in the first sentence. Id. at 11 n. 1.
     
      
      . Apprendi v. New Jersey, 530 U.S. 466, 477, 120 S.Ct 2348, 147 L.Ed.2d 435 (2000) (quoting United States v. Gaudin, 515 U.S. 506, 510, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995)).
     
      
      . This conclusion might appear remarkably like a rule that failure to specify the burden of 1 proof in relation to a special interrogatory is automatically subject to reversal, so no harmless-error analysis is required (following Sullivan rather than Neder). Nevertheless, there could be some situations in which the failure to specify the standard of proof might be harmless (for example if the court listed the standard of proof only in the overview and did not repeat it for each of the various counts). We express no view on such hypo-theticals.
     
      
      . Stanford attempts to rebut that evidence by pointing to testimony that he was present for only part of those discussions, and he also claims that he did not have the scientific training to assess the chemical similarity of the two drags.
     
      
      . Nevada v. Jackson, — U.S. —, 133 S.Ct. 1990, 1992, 186 L.Ed.2d 62 (2013) (quoting Crane v. Kentucky, 476 U.S. 683, 690, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986)). See also Holmes v. South Carolina, 547 U.S. 319, 324, 126 S.Ct. 1727, 164 L.Ed.2d 503 (2006) (noting that this right could be rooted in the Due Process Clause or in the Compulsory Process or Confrontation Clause of the Sixth Amendment).
     
      
      . United States v. Ramos, 537 F.3d 439, 448 (5th Cir.2008) (quoting United States v. Mizell, 88 F.3d 288, 294 (5th Cir.1996)).
     
      
      . Id.; see also Crane, 476 U.S. at 691, 106 S.Ct. 2142. Cf. Neder, 527 U.S. at 15, 119 S.Ct. 1827; McFadden, 135 S.Ct. at 2307, both holding that a district court’s omission of a required element (albeit in the context of jury instructions) is reviewed for harmless error.
     
      
      . Where a district court rules that proof of a required element is not necessary, a claim that a defendant was denied the ability to present a complete defense is essentially the inverse of a claim that the jury instructions were inadequate. We have observed the close relationship between these two claims in the context of the refusal to deliver a defense-requested jury instruction. The third prong of our test for error in this regard is whether the requested instruction "concerns an important point in the trial so that the failure to give it seriously impaired the defendant’s ability to effectively present a given defense.” United States v. John, 309 F.3d 298, 304 (5th Cir.2002) (quoting United States v. Grissom, 645 F.2d 461, 464 (5th Cir. Unit A May 1981)).
     
      
      
        .See, e.g., United States v. Skelton, 514 F.3d 433, 445 n. 7 (5th Cir.2008) (determining that a district court’s limitations on cross-examination violated the right to present a complete defense).
     
      
      . The government also claims that at least one district court has "rejected” Reinhold’s testimony in a case involving AM-2201 case, although that is not entirely accurate. In United States v. Bays, No. 3:13-CR-0357-B, 2014 WL 3764876, at *8 (N.D.Tex. July 31, 2014), the court distinguished the defendant’s interpretation of a statement, made by Reinhold, that was used in an evidentiary exhibit submitted by the government. It did not “reject” Reinhold’s testimony but noted that "substantial similarity is not a scientific question and there is no requirement that experts agree on its exact definition.” Id.
      
     
      
      . Nonetheless, Stanford also contends that the court denied him the ability to rebut a finding of knowledge by sustaining an objection to his question of when Francis "kn[e]w that AM-2201 was an analogue.” Stanford claims that if Francis did not know AM-2201 was an analogue, there was no way he could have informed Stanford that it was an analogue. The court ruled that this question went to the ultimate issue of whether AM-2201 was an analogue, so it barred Francis from answering. Even assuming that this testimony would have made a difference in Stanford’s ability to rebut a finding of knowledge, the ruling appears correct. A significant part of the case was a determination that AM-2201 was an analogue, and Federal Rule of Evidence 704 was not "intended to allow a witness to give legal conclusions.” Owen v. Kerr-McGee Corp., 698 F.2d 236, 240 (5th Cir.1983).
     
      
      . This does not mean that all of Stanford’s attempts to rebut a finding of knowledge must be allowed in the event of a retrial on remand. The court should apply the normal rules of evidence to the admission of testimony. See Ramos, 537 F.3d at 448 (explaining that the right to present a complete defense “is limited and must be weighed against the countervailing interests in the integrity of the adversary process”).
     
      
      . Stanford claims that, after trial, he obtained "his own telephone records” that, he says, prove that Francis’s "calls to Stanford in late August 2011” were "lies.” The government contends that this evidence was "newly discovered.” Under the “Berry rule,” see Berry v. Georgia, 10 Ga. 511 (1851), if the basis for the motion requesting a new trial is newly discovered evidence, the defendant must show
      (1) that the evidence is newly discovered and was unknown to him at the time of trial; (2) that the failure to discover the evidence was not due to his lack of diligence; (3) that the evidence is not merely cumulative, but is material; and (4) that the evidence would probably produce an acquittal.
      
        United States v. Turner, 674 F.3d 420, 429 (5th Cir.2012) (quoting United States v. Blackthorns, 378 F.3d 449, 452 (5th Cir.2004)). In Napue cases, the fourth factor is relaxed from requiring evidence that "would probably produce an acquittal” to creating "any reasonable likelihood that the false testimony affected the judgment of the jury.” Wall, 389 F.3d at 473.
      Because his phone records were already in the government’s possession at the time of trial (and presumably because he had access to them as well), Stanford urges that they cannot be "newly discovered.” Yet, he misapprehends the Berry rule. The fact that he could have obtained his phone records merely demonstrates that he fails the Berry test, and there was no justification for a new trial. See United States v. Riley, 544 F.2d 237, 240 (5th Cir.1976).
      Stanford’s claim also appears disingenuous. His reply brief to the government's opposition to his request for a new trial referred to “newly discovered information” and attached the telephone records. Thus, apart from the materiality problems discussed above, there is an additional reason to deny Stanford’s Na-pue claim based on the telephone calls.
     
      
      . Nevertheless, Stanford was not given a chance to impeach Barrow with these business records, because the court ruled that they were inadmissible for lack of notice by Stanford under Federal Rule of Evidence 902(11). Even if that ruling was error, as Stanford contends, the conflict between Barrow's testimony and Stanford’s business records is not material, as we have said.
     
      
      . The $19,000 check written by Buswell/Cu-rious Goods stated "Boyd’s RCA dues to be deducted from Miyagi bill,” implying, without directly saying so, that that check was for both of their RCA dues. Stanford claims that Barrow never gave Curious Goods the referenced deduction.
     
      
      . See Phillips v. Omoski, 673 F.3d 1168, 1188-89 (9th Cir.2012); Jackson v. Brown, 513 F.3d 1057, 1076 (9th Cir.2008).
     
      
      . See Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). In his briefing, Stanford also argued that the government failed to disclose material required by the Jencks Act, but he abandoned that claim at oral argument.
     
      
      
        . See United States v. Williams-Davis, 90 F.3d 490, 514 (D.C.Cir.1996) (quoting United States v. Ramos, 27 F.3d 65, 71 (3d Cir.1994)); see also United States v. Griffin, 659 F.2d 932, 939 (9th Cir.1981).
     
      
      . Ramos, 27 F.3d at 70 (quoting United States v. Harrison, 524 F.2d 421, 427 (D.C.Cir.1975)).
     
      
      . For example, Stanford claims that at the second trial the government placed statements that he allegedly made about his supposed agreement with the attorney general much earlier in the conspiracy than it had at the first trial. Stanford argues that the government’s case increased notably after Bus-well’s guilty plea, but the government failed to call Buswell at trial, "likely because he lacked credibility.” In other words, Stanford implies that Buswell was lying and that those lies were passed on to the other witnesses who testified against Stanford.
     
      
      . Cf. United States v. McKinney, 758 F.2d 1036, 1052 (5th Cir.1985) ("McKinney does not point to specific documents that may contain exculpatory evidence.”).
     
      
      . At oral argument, Stanford’s counsel agreed that any McFadden error affects only Count One. Thus, the reversal on that court has no effect on the sentence related to any other counts.
     
      
      . United States v. Robinson, 741 F.3d 588, 598 (5th Cir.2014) (quoting United States v. Cisneros-Gutierrez, 517 F.3d 751, 764 (5th Cir.2008)).
     
      
      . Id. (quoting United States v. Neal, 578 F.3d 270, 273 (5th Cir.2009)).
     
      
      . United States v. Fuentes, 775 F.3d 213, 218 (5th Cir.2014) (per curiam); see also United States v. Alaniz, 726 F.3d 586, 618 (5th Cir.2013). But see Robinson, 741 F.3d at 598 (holding that harmless-error review applies to step one (procedural reasonableness) and abuse-of-discretion review to step two (substantive reasonableness)).
     
      
      . United States v. Brooks, 681 F.3d 678, 712 (5th Cir.2012); see also Robinson, 741 F.3d at 598; Fuentes, 775 F.3d at 218.
     
      
      . See Teague v. City of Flower Mound, 179 F.3d 377, 383 (5th Cir.1999). Likewise, we are foreclosed from evaluating United States v. Hossain, No. 15-cr-14034, 2016 WL 70583 (S.D.Fla. Jan. 5, 2016), which Stanford cites, in which the district court chose to vary from the 1:167 ratio based on Cozzi's testimony.
     
      
      . The government urges that Stanford failed to preserve his Kimbrough claim because "he never specifically objected on the ground that the district court misunderstood the nature and extent of its discretion in that regard.” The government made the same argument in Malone. See United States v. Malone, No. 14-31426, Brief of Appellee at 20-21. There, we did not consider whether this claim called for plain-error review, nor did we discuss the appropriate standard of review. See Malone, 809 F.3d at 258-60. It would not be proper here to apply a plain-error standard to the Kimbrough claim to reach a different conclusion (i.e. that the district court’s statement was not ambiguous).
     
      
      . Stanford contends that the district court’s rejection in Malone of the government’s recommendation for a downward departure under U.S.S.G. § 5K1.1 carries "more weight” in the harmless-error analysis than does the rejection of his request for a below-guidelines sentence here. Nevertheless, the court did more than reject Stanford’s request for a lower sentence — it affirmatively explained why it thought its chosen sentence was appropriate.
     
      
      . Stanford bases this argument on Burns v. United States, 501 U.S. 129, 136, 111 S.Ct. 2182, 115 L.Ed.2d 123 (1991). Nevertheless, Bums dealt with a district court's determination to depart from the guidelines sua sponte, which the Court held required notice to the parties. Bums did not deal with a court's decision to apply one method of calculation found in the guidelines instead of another. In any case, in Irizarry v. United States, 553 U.S. 708, 715, 128 S.Ct. 2198, 171 L.Ed.2d 28 (2008), the Court overruled Bums.
      
     
      
      . United States v. Garcia, 797 F.3d 320, 323 (5th Cir.2015) (quoting United States v. Angeles-Mendoza, 407 F.3d 742, 749 n. 12 (5th Cir.2005)); see also Irizarry, 553 U.S. at 715, 128 S.Ct. 2198 ("Sound practice dictates that judges in all cases should make sure that the information provided to the parties in advance of the hearing, and in the hearing itself, has given them an adequate opportunity to confront and debate the relevant issues.”).
     
      
      . 3 Charles A. Wright & Sarah N. Welling, Federal Practice & Procedure: Criminal § 529 (4th ed.2011). See also Irizarry, 553 U.S. at 715, 128 S.Ct. 2198 (noting the "factual basis for a particular sentence” that can come as a surprise and create potential notice problems).
     
      
      . At issue was testimony the court considered from a different criminal trial that was not included in the PSR. Garcia, 797 F.3d at 325.
     
      
      . The PSR also stated that Stanford should be held accountable for $4,202,332 of the conspiracy proceeds and relied on that number in calculating the base offense level for the money-laundering group. Stanford objected at the sentencing hearing, and the court agreed, ruling that the “base offense level should be based on the actual amount that Mr. Stanford was found by the jury to launder of $143,000.’’ If Stanford had no problem with the court’s relying (based on his own objection) on these different facts (i.e. the different dollar amount) to calculate the base offense level, he likewise should have no issue with the court's decision (based on the gov-emment’s objection) to apply a different rule to calculate the base offense level.
     
      
      . Cf. United States v. Zelaya-Rosales, 707 F.3d 542, 545 (5th Cir.2013) (holding that even though the court’s lack of notice regarding its intent to depart upward from the guidelines was in error, it did not affect the defendant’s substantial rights when he did not dispute the accuracy of the facts that led to the variance nor demonstrate "a reasonable probability that the district court would have imposed a lesser sentence if it had given him notice of its intent to depart from the Guidelines”).
     
      
      . Stanford does not dispute the conviction of a conspiracy to violate § 1957(a).
     
      
      . It is only Stanford’s conviction for a conspiring to violate § 195 6(a)(1)(A)© that could provide the basis for the two-level enhancement. Although he was generally convicted under Count Three for violating § 1956(h), the application notes instruct that the two-level enhancement for convictions under § 1956 found in Section 2S 1.1 (b)(2)(B) does not apply “if the defendant was convicted of a conspiracy under 18 U.S.C. § 1956(h) and the sole object of that conspiracy was to commit an offense set forth in 18 U.S.C. § 1957.” U.S.S.G. § 2S1.1, application note 3(C).
     
      
      
        .United States v. Brown, 553 F.3d 768, 782 (5th Cir.2008) (quoting United States v. Miles, 360 F.3d 472, 477 (5th Cir.2004)).
     
      
      . This is why Stanford's discussion of Brown, 186 F.3d at 670, is not on point. At issue there was a downstream transaction— using funds already obtained from illicit activities to pay legitimate business expenses. We specifically noted that the government could have prosecuted the initial act of receiving and depositing illicit funds even if it could not prosecute for later spending those dirty funds on legitimate business activities. Id. at 668 n. 12. Here, the issue is the initial receipt of illicit funds for the purposes of furthering criminal activity, not how Stanford spent the funds after receiving them.
     
      
      . Even without the conviction under Count One, Stanford knew that he was promoting illicit activities by supporting the conspiracy in such a manner. As his conviction under Count Two (which he does not challenge) demonstrates, he was well aware that the conspiracy was unlawful by introducing mis-branded drugs into interstate commerce.
     
      
      . Alternatively, Stanford maintains that because the verdict form for Count Three did not allow the jury to specify whether it was finding him guilty of conspiring to engage in money-laundering under § 1956(a)(l)(A)(i) or under § 1957, it violated his rights under Apprendi. Stanford makes this argument for the first time in his reply brief, so it is waived. See Flex Frac Logistics, L.L.C. v. N.L.R.B., 746 F.3d 205, 208 (5th Cir.2014) (explaining that "arguments raised for the first time in a reply brief are waived”); Fed. R.App. P. 28(a)(8)(A).
     