GREGG COSTA, Circuit Judge:

Running a profitable small business is notoriously difficult. But the clients of a tax preparation service run by a husband and wife, Gladstone and Jacqueline Morrison, brought business failure to a new level. Year in and year out, the vast majority of the clients submitted tax returns showing sizable business losses. A federal jury provided the following explanation for this seeming anomaly of unlucky clients: the Morrisons helped their clients prepare returns with fake business losses so the clients could obtain refunds rather than pay the taxes they owed.

That was not the only fraud the jury found. Once they became aware of an IRS investigation into their business, the Morrisons attempted to rid themselves of the problem by selling the business on multiple occasions. Not only did those sales not insulate the Morrisons from tax fraud charges, but they resulted in additional charges of wire fraud because the Morrisons made numerous misrepresentations in connection with these deals, including falsely stating that the business was not the subject of any ongoing investigation.

The Morrisons appeal their convictions for conspiring to submit fraudulent tax returns, aiding and abetting the filing of numerous false returns, and wire fraud in connection with the attempted sales of the business. They both challenge the sufficiency of the evidence. They also raise, among other arguments, separate challenges to the district court's conduct during the trial. Jacqueline contends that the district court impermissibly limited her testimony. Gladstone contends that the district court assisted the prosecution. Finding no reversible error, we affirm.

I.

Jacqueline and Gladstone started a tax preparation firm called Jacqueline Morrison & Associates, or JMA, in 2005. Jacqueline was the accountant. Gladstone came from an engineering background and taught himself how to prepare taxes. The business started small and included staff who had never prepared taxes before, including the Morrisons' family and friends.

JMA first came to the attention of the IRS because it filed tax returns without W-2 forms. But in 2008, during a compliance visit following up on the W-2 issue, an IRS agent noticed that there was an unusually high number of Schedule C tax forms being filed on behalf of JMA clients. Schedule C forms are used to record income or losses from a sole proprietorship. Although small businesses have a high failure rate, it is unusual for a Schedule C form to show substantial losses for multiple years because most personal businesses would not continue to operate with recurring annual losses. Although consistent losses do not make for good business, they do reduce tax liability. And for a number of JMA clients, the Schedule C losses reduced income enough to make them eligible for the earned income tax credit.

The vast majority of JMA's clients filed Schedule C forms, ranging from 92.5% of clients in 2006 to 74.4% in 2009. This is a much higher rate than the general population of taxpayers. Nationally only about 21% of taxpayers filed Schedule C forms, with that number rising slightly to just over 23% in the Dallas-Fort Worth metroplex where JMA was located. The returns of JMA clients look even more suspicious when the numbers on those Schedule C forms are considered. Between 2006 and 2009, an average of 61.4% of JMA clients filing Schedule Cs showed losses, whereas only 4.6% of national Schedule C filers showed losses (and 6.5% of those in the Dallas-Fort Worth region).

Many of JMA's clients testified at trial about how the losses reported on their returns were grossly overstated or simply fictitious. For example, Rosland McFadden was a full-time teacher who also sold Avon and Mary Kay products on a small scale. In 2009, her Schedule C form showed income of $2,508 from "cosmetic services" and expenses of $39,243 for a net loss of $36,735. Her JMA-prepared Schedule C forms showed similar losses in prior years even though she testified that she had no expenses from the side business.

JMA reaped a significant benefit from the creation of fraudulent Schedule C forms. It charged higher fees for the creation of the Schedule C. The refunds that often resulted were an easy source of payment to JMA as its fees were debited directly from the refunds. Perhaps most significantly, submitting returns with the false losses fostered loyalty from customers who liked the refunds and referred others to JMA.

An undercover IRS agent's visit to JMA also revealed how the business worked. Given the information the agent provided when he asked JMA to prepare his taxes, his refund should have been about $200. But when he feigned disappointment at that low number, a JMA employee suggested the refund could be increased if he had an outside business. Despite the agent responding that he had no such business, the JMA employee created a daycare business and fabricated its expenses. The result was a refund of more than $2,000.

The seriousness of the IRS investigation became apparent when agents executed warrants at JMA's offices and the Morrisons' home in May 2010. About a month later, the Morrisons tried to distance themselves from what they now realized was a problem. They agreed to a franchise agreement with Express Tax, an H&R Block subsidiary, under which they gave up some ownership in the business, which would now be an Express Tax franchise, for $295,000. As part of the deal, Express Tax also obtained JMA's client list. During the negotiations, the Morrisons misrepresented that they were not under investigation.

After entering into the franchise agreement with Express Tax, the Morrisons sought a purchaser for the new franchisee and found Vernaljay Haney. After buying the business from the Morrisons, Haney met with Express Tax and realized he had purchased some things from the Morrisons that they no longer owned. The Morrisons had agreed to sell their client list and the whole company to Haney, but Express Tax already owned the client list and a 22.5% interest in the company. After Haney brought this problem to their attention, the Morrisons reduced the purchase price. When Haney's third installment of that price was due, Express Tax advised Haney not to pay, asserting that it, rather than the Morrisons, was entitled to the payment. Haney agreed with Express Tax and did not make the third payment to the Morrisons.

But Gladstone devised another way to receive the third installment. He asked for Haney's identification number for electronic tax filing purportedly because he was going to help Haney purchase and register tax software. Instead, Gladstone used Haney's number to change the location where JMA's preparer's fees would be deposited, rerouting the money from the business' account (now controlled by Haney) to the Morrisons'. Over $100,000 was transferred to the Morrisons before Haney realized the accounts had been changed.

After the unauthorized change of accounts, Haney left JMA, and the Morrisons sought a new purchaser. They found David Awe. In their negotiations with Awe, the Morrisons again signed a contract stating: "there are no legal actions, suits, claims, investigations, arbitrations or other legal administrative or governmental proceedings pending or threatened against the seller, nor does the seller know or have any reasonable grounds to know of any basis for the foregoing."

After Awe assumed ownership, several clients reported they were being audited. The Morrisons assured Awe this was just "part of the normal audit process." Awe's own investigation revealed that nearly all the prior year's returns had Schedule Cs filed. He stopped the practice of filing fraudulent Schedule Cs which resulted in the loss of clients. Once Awe learned of the extent of the fraud, he told the Morrisons he was not going to make further payments until after he evaluated the business at the end of tax season. Ultimately Awe did not make further payments.

The IRS investigation resulted in a grand jury charging the Morrisons with conspiracy to prepare false returns (18 U.S.C. § 371 and 26 U.S.C. § 7206(2)), aiding and abetting in the assisting of preparing fraudulent returns (18 U.S.C. § 2 and 26 U.S.C. § 7206(2)), and multiple counts of wire fraud (18 U.S.C. § 1343).

After a three day trial, a jury found the Morrisons guilty on all counts. The district court sentenced both defendants to a below-Guidelines prison term of 187 months. Both of them were also ordered to pay restitution of $17,807,106.

II.

The Morrisons challenge the sufficiency of the evidence on all counts, but Jacqueline's challenges to her conspiracy and wire fraud convictions are not sufficiently developed for us to consider. United States v. Thames, 214 F.3d 608, 611 n.3 (5th Cir. 2000) (a party waives an issue if he fails to adequately brief it); see also FED. R. APP. P. 28(a)(8)(A) (Appellant's brief must contain his "contentions and the reasons for them, with citations to the authorities and parts of the record on which the appellant relies...."). For the other convictions, we review the sufficiency of the evidence de novo. United States v. Churchwell, 807 F.3d 107, 114 (5th Cir. 2015). That evaluation views "all of the evidence in the light most favorable to the verdict to determine whether any rational trier of fact could find guilt beyond a reasonable doubt." Id.

A

We will uphold Gladstone's conspiracy conviction if there was sufficient evidence to support the findings that: (1) he agreed with another person to pursue an unlawful objective; (2) he joined the conspiracy knowing of its unlawful objective; and (3) at least one member of the conspiracy committed an overt act in furtherance of it. United States v. Mann, 493 F.3d 484, 492 (5th Cir. 2007). He contends there was insufficient evidence of an agreement, placing the blame on Jacqueline as the primary actor.

Gladstone was the Chief Operating Officer of JMA and "over[saw] the entire operation." He created multiple forms used at JMA including verification forms and the Schedule C due diligence forms. Haney, the purchaser of JMA who then learned about the false Schedule Cs, testified that his investigation revealed that the practice of filing fraudulent returns originated with "Jackie and Gladstone." Perhaps the most damning evidence of Gladstone's involvement was that he prepared tax returns for at least one client, Stefanie Brown, that falsely showed the large Schedule C losses typical of so many other clients' returns. There was also evidence from which the jury could have concluded that Gladstone worked with his wife to prepare their personal and business tax returns that grossly understated their income. And Gladstone's substantial involvement in the fraud relating to the attempted sales of the business is evidence not just of his central role in JMA, but also evidence the jury could use to infer a similar knowledge and fraudulent intent concerning the contemporaneous tax return fraud. Cf. FED. R. EVID. 404(b) (recognizing that even uncharged similar acts can be probative of a defendant's intent and knowledge concerning charged offenses); United States v. Watson, 433 Fed.Appx. 284, 287 (5th Cir. 2011) (recognizing that defendant's uncharged conduct of filing false tax returns for himself and his wife was probative on whether he had intent to prepare false tax returns for his clients).

Because an agreement to be part of a conspiracy need not be explicit and "may be inferred from a `concert of action,'" United States v. Mann, 161 F.3d 840, 847 (5th Cir. 1998), this evidence is more than sufficient to support the jury's finding that Gladstone was part of a conspiracy to file false tax returns. See United States v. Mudekunye, 646 F.3d 281, 284-85 (5th Cir. 2011) (finding sufficient evidence of a conspiracy when defendant worked as a tax preparer, had a cubicle at the tax office at the center of the conspiracy, had multiple clients, and prepared fraudulent returns in the same manner as his co-conspirators).

B

The convictions on the substantive counts of filing false tax returns should be upheld if there was sufficient evidence to support jury findings that: (1) each defendant aided, assisted, counseled, or advised another in the preparation of the tax return in question; (2) the tax return contained a statement falsely claiming income, deductions, or tax credits; (3) the defendant knew that the statement was false; (4) the false statement was material; and (5) the defendant acted willfully. 26 U.S.C. § 7206(2); United States v. Clark, 577 F.3d 273, 285 (5th Cir. 2009).

Although the taxpayers whose returns were at issue in all of the thirteen substantive counts on which Jacqueline was convicted testified that the returns were false, Jacqueline argues the testimony was not credible. She tries to identify "contradictory admissions" by several witnesses from which she concludes that the jury should "not have given much weight" to their testimony. That runs directly counter to the principle that credibility determinations and weighing of evidence are the province of the jury, not appellate judges. Mudekunye, 646 F.3d at 286 (recognizing that it is not this court's "role to evaluate witness credibility — that, of course, is for the jury").

Her attack on the statistical evidence cited above, which shows the abnormally high number of clients filing Schedule Cs and even more unusually high percentage of those forms that show losses, suffers from the same flaw. She points out reasons why she believes the jury should not have given it much weight, such as the socioeconomic status of JMA's clientele or fact that the statistics were not limited to filers who used tax preparation firms. Those are points to be raised on cross examination, indeed her counsel made the first point, but that does not prevent the jury from considering the data along with the other mass of evidence showing Jacqueline's involvement in filing false Schedule Cs. That includes testimony from clients that Schedule C forms Jacqueline prepared showed grossly overstated or simply fictitious losses, and that such losses if accurate would not have allowed the business to continue operating. The evidence supports her conviction on all the substantive tax counts.

Gladstone challenges his convictions on the substantive tax counts on the ground that he did not prepare most of the tax returns — Jacqueline did. Indeed, his lack of direct involvement with the returns at issue in all but two of those counts (counts 13 and 14, which are for the returns of Stefanie Brown who testified that Gladstone was her preparer) makes his sufficiency challenge a much closer call. A defendant, however, "does not have to sign or prepare the return to be amenable to prosecution" under section 7206(2). United States v. Wolfson, 573 F.2d 216, 225 (5th Cir. 1978). That statute incorporates aiding and abetting liability by making one guilty who "[w]illfully aids or assists" in the filing of false returns. 26 U.S.C. § 7206(2); United States v. Searan, 259 F.3d 434, 443-44 (6th Cir. 2001) ("The recognition that the first element of a § 7206(2) charge effectively incorporates `aiding and abetting' complicity liability means that charging a defendant with `aiding and abetting,' under 18 U.S.C. § 2, the `aid[ing], assist[ing], procur[ing] ...' of false tax returns, under 26 U.S.C. § 7206(2) is a redundancy.").1 Section 7206(2) thus "relies on a theory of liability akin to complicity: it criminalizes an act that facilitates another person's crime when the act is undertaken willfully and with knowledge of the circumstances that make the other person's act illegal." Clark, 577 F.3d at 285 (quoting Searan, 259 F.3d at 443).

Although the false return statute does not limit liability "to return preparers" but instead "reaches all knowing participants in the fraud," id. (quoting United States v. Fletcher, 322 F.3d 508, 514 (8th Cir. 2003)), Gladstone correctly points out that most of our cases addressing it involve defendants who have prepared returns, signed them, or had some other link to a specific return. See Mudekunye, 646 F.3d at 286 (upholding conviction when defendant was the tax preparer working with clients); United States v. Baker, 522 Fed.Appx. 244, 247 (5th Cir. 2013) (holding evidence was sufficient when taxpayers testified that defendant prepared their returns); United States v. Statin, 367 Fed. Appx. 492, 495-96 (5th Cir. 2010) (holding that defendant's signature on return was sufficient evidence even when defendant did not prepare return). And he relies on our statement in an unpublished opinion that the statute's "aiding and assisting" language "requires joining [the defendant] factually to a return." Statin, 367 Fed. Appx. at 495.

But such a requirement is inconsistent with our precedential case law construing section 7206(2) and that of other circuits, as well as general aiding and abetting principles. To be convicted under an aiding and abetting theory, the defendant must "share[ ] in the principal's criminal intent" and take some affirmative steps "to aid the venture or assist[ ] the perpetrator of the crime." United States v. Garcia, 242 F.3d 593, 596 (5th Cir. 2001) (examining sufficiency of aiding and abetting evidence in drug case). He "must have aided and abetted each material element of the alleged offense[s]." United States v. Lombardi, 138 F.3d 559, 561 (5th Cir. 1998) (examining sufficiency of evidence of aiding and abetting the use of a minor in a drug offense conviction).

Relying on these principles in the context of the false tax return statute, the Sixth Circuit rejected an argument like Gladstone's when a son argued that his mother prepared and signed most of the returns in question. Searan, 259 F.3d at 445. Using evidence adduced to support the overarching conspiracy conviction, the court upheld guilty verdicts on the substantive counts based on evidence that the son actively participated in the criminal acts by assuring victims of his mother's competency, prepared certain fraudulent returns himself, held himself out to be a partner in the business, and split profits. Id.; see Nye & Nissen v. United States, 336 U.S. 613, 619, 69 S.Ct. 766, 93 L.Ed. 919 (1949) (explaining that the "fact that some of th[is] evidence" supporting aiding and abetting liability "may have served double duty by also supporting the charge of conspiracy is of course immaterial").

Like Searan, a case we have relied on before in interpreting this statute, see Clark, 577 F.3d at 285 (quoting Searan, 259 F.3d at 443), much of the evidence underpinning Gladstone's conspiracy convictions supports his guilt on the substantive counts as an aider and abettor.2 As previously recounted, Gladstone co-owned the business with Jacqueline, was the Chief Operating Officer, and oversaw the entire operation. He prepared the false returns for Stefanie Brown, (the subject of counts 13 and 14) that suffered from the same fraudulently-inflated Schedule C losses as those that Jacqueline prepared (counts 3-12). Gladstone also created false tax returns for himself and Jacqueline which grossly underreported their taxable income. Recognizing that Gladstone's connection to counts 3 through 12 is less direct than what we have seen in other section 7206(2) cases, we nonetheless conclude that his active involvement in, and knowledge of, the scheme were sufficient evidence from which a jury could find that he knowingly assisted in the submission of these false returns. Clark, 577 F.3d at 286.

C

Consistent with his significant involvement in the transaction with Express Tax, Gladstone only attacks the jurisdictional element of that wire fraud conviction. He argues that the wire transfer of $295,000 to pay for the franchise agreement did not cross state lines. Although the documentation concerning the wire did not identify the bank's location where the transfer originated, it did specify that the originating bank account was held by H&R Block's Kansas City branch. And testimonial evidence from a bank witness that the wire was sent from Kansas City to Fort Worth suffices.

Gladstone's challenge to his wire fraud conviction relating to the sale of JMA to Vernaljay Haney makes a similar mistake of discounting the worth of testimony. This is the count charging Gladstone with fraudulently using Haney's electronic filing number to divert JMA's preparer fees from a Haney account to a Morrison one. It was disputed at trial whether the form Gladstone signed that used Haney's number amounted to a representation that the number belonged to Gladstone. Gladstone argued that his signature verified only that he was an owner of JMA, not the owner of the number. But a representative from the bank disagreed with that characterization, explaining that an employee receiving the form would believe that the signatory is representing that he is the authorized user of that electronic filing number. And the document alone supports that impression. We therefore decline Gladstone's invitation to reweigh this evidence. United States v. Holmes, 406 F.3d 337, 351 (5th Cir. 2005).

As to the final wire fraud counts involving the sale to Awe, Gladstone contends that there was no fraud because David Awe got the "benefit of his bargain." The evidence presented at trial tells a different story. Gladstone (and Jacqueline) signed a contract stating that the company was not under investigation. Awe thus thought he was buying an above-the-board business. Instead, he got one that was under investigation for the fraud that a jury later found was rampant. Because much of the attraction of clients to JMA was the refunds that resulted from the fraud, uncovering the fraud unsurprisingly reduced business. The lie about whether JMA was under investigation was certainly material. See Neder v. United States, 527 U.S. 1, 16, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (analyzing materiality of false statement under section 7206(1)).

The evidence supports all of Gladstone's wire fraud convictions.

III.

The defendants bring separate claims alleging errors in the district court's conduct during the proceeding.

A

Jacqueline challenges the time limit the district court imposed on her testimony. Apparently dissatisfied at the pace of trial, halfway through the government's case-in-chief, the court began imposing time limits. It did so by going through the witness lists and asking the propounding attorney how long the direct exam would take for each. The court then imposed a limit for direct exam based on the attorney estimate and gave the opposing side the same time for cross examination. The district court enforced those limits during examination for both the government and defense with comments like, "you're about out of time."

The court was more flexible when it came to Jacqueline's testimony, which began at the end of the second day of trial. It did not impose a time limit at the outset. After 40 minutes, the district court asked how much longer defense counsel needed to finish questioning. Counsel responded, "maybe 45 minutes," and the court adjourned for the night. The following day, after further direct examination, the district court told defense counsel, "you've been at it about 50 minutes today. I think yesterday you indicated it would probably be another 45 minutes at some point in time. Are you almost through?" Defense counsel responded — "I was grossly mistaken in my estimate of the time it would take. I apologize, Your Honor. I just didn't know." The district court then instructed counsel to "focus on the real issues" and that he was limiting counsel to "15 minutes to finish," but counsel stated that he could not finish in that time. The judge then inquired again how long counsel thought it would take to complete questioning and counsel responded, "I don't want to say and then be wrong again. I don't know." In response, the district court said, "Well, then I don't know any way to do it but give you a time limit. I'll give you 20 minutes, and that's the answer. So you need to focus on what you're doing and what's important." Defense counsel resumed questioning. After the additional 20 minutes, the district court told counsel his time had expired, and direct examination ended.

At this point, defense counsel moved for a mistrial and asked to make an offer of proof at the end of the case, but the district court denied that request and instead asked for a contemporaneous offer of proof. Defense counsel declined, stating it would be impossible to do so. The district court denied the motion for mistrial. Almost two weeks after trial, Jacqueline made a "supplemental offer of proof."

Imposing time limits during trial is a growing trend among district courts. In an age of vanishing jury trials, a development that likely results at least in part from the increased length and cost of trials, time limits are one tool that courts have to make trials more efficient and juror friendly. See JURY INNOVATIONS PROJECT: AN EFFORT TO ENHANCE JURY TRIALS IN TEXAS STATE AND FEDERAL COURTS, at 16-17, 75-78 (suggesting new procedures for civil trials, including time limits, that increase juror comprehension) http://www.txs.uscourts.gov/sites/txs/files/PilotProgramManual.pdf. We have thus approved their use, so long as the limits are reasonable, even in criminal cases where limits are more controversial.3 United States v. Colomb, 419 F.3d 292, 299 (5th Cir. 2005) ("[A] district court may impose reasonable time limits on the presentation of evidence and the examination of witnesses."); United States v. Gray, 105 F.3d 956, 963-65 (5th Cir. 1997) (noting that a district court judge has broad discretion in managing his docket including "imposition of time limits on counsel"). Other circuits take a similar approach. See United States v. Spangler, 638 Fed.Appx. 611, 613 (9th Cir. 2016) (finding time limit on defense counsel's cross examination of a witness does not violate Confrontation Clause unless it "limits relevant testimony and prejudices the defendant, and denies the jury sufficient information to appraise the biases and motivations of the witness"); United States v. Vest, 116 F.3d 1179, 1187 (7th Cir. 1997) ("The District Court's time limits were reasonably anchored to the defendant's own requests for time and to the amount of time the Government used on direct" and "[t]he district court's willingness to bend the time limits shows flexibility...."). If anything, it seems that time limits in criminal cases will generally pose more of a challenge for the prosecution as it typically presents far more of the evidence given that it has the burden of proof.

In Jacqueline's trial, however, she contends that the limits hurt the defense. She recognizes that we have generally allowed reasonable time limits in criminal cases but argues that limiting a defendant's testimony raises special constitutional concerns. To be sure, constitutional concerns are implicated when a defendant testifies. See Rock v. Arkansas, 483 U.S. 44, 51, 107 S.Ct. 2704, 97 L.Ed.2d 37 (1987) ("The right to testify on one's own behalf at a criminal trial has sources in several provisions of the Constitution."). But as is often the case, the right "may, in appropriate cases, bow to accommodate other legitimate interests in the criminal trial process" so long as those restrictions on the defendant's right to testify are not arbitrary. Id. at 55-56, 107 S.Ct. 2704 (citation omitted). Indeed, in a broad sense, any time limits imposed on defense counsel at trial may come into conflict with another constitutional right at least as important as the right to testify in one's own defense: the Sixth Amendment right to confront witnesses.4 See United States v. Bensimon, 172 F.3d 1121, 1128 (9th Cir. 1999) (recognizing this tension yet allowing limits on defense counsel's examination of adverse witnesses). Yet we have allowed time limits that do not unreasonably curtail a defendant's right to examine government witnesses and present an effective defense. Gray, 105 F.3d at 963-65. We are thus not sure whether special rules — that is, a rule beyond the important reasonableness requirement for all time limits — should govern time limits for a defendant's own testimony.5

We need not decide that question here because defense counsel did not make an offer of proof sufficient to preserve the objection to the exclusion of testimony.

United States v. Wen Chyu Liu, 716 F.3d 159, 170-71 (5th Cir. 2013) (quoting 1 Jack B. Weinstein & Margaret A. Berger, WEINSTEIN'S FEDERAL EVIDENCE § 103.20(4) (emphasis in original)); see also United States v. Winkle, 587 F.2d 705, 710 (5th Cir. 1979) (citations omitted) ("[T]his circuit will not even consider the propriety of the decision to exclude the evidence at issue, if no offer of proof was made at trial.").

The failure to offer any information about what questions counsel still needed to ask Jacqueline when the court ended the direct examination matters for multiple reasons. First, such an offer of proof would have allowed the district court to reconsider its ruling if counsel indicated he had to elicit testimony about topics that had not already been covered. Indeed, the court had already shown a willingness to be flexible by allowing 25 more minutes of testimony beyond defense counsel's original estimate, resulting in a total 110 minutes of testimony. Second, the lack of a contemporaneous offer of proof limits our ability on appellate review to determine whether the exclusion was harmful. Wen Chyu Liu, 716 F.3d at 171 (refusing to consider offer of proof made in motion for new trial and limiting review to the trial record to determine whether exclusion of expert witness was error). And an offer of proof submitted two weeks after trial, by which time counsel no doubt has engaged in quite a bit of Monday-morning quarterbacking, does not provide what an offer of proof is supposed to: an alternative view of what the trial would have looked like if the court had ruled differently. See Winkle, 587 F.2d at 710.

Yet even if we were to consider Jacqueline's offer of proof, we would not find a basis for reversal. The evidence against Jacqueline was overwhelming and although trial counsel may not have delved into as much detail as he wanted, he did cover the main topics outlined in his posttrial offer of proof during the almost two hours he questioned Jacqueline. We thus cannot say that the district court committed any reversible error in limiting Jacqueline's testimony.6

B

Jacqueline also challenges the district court's denial of her motion to recuse, which she filed after trial but before sentencing.7 We review the denial of a motion to recuse for abuse of discretion. Brown v. Oil States Skagit Smatco, 664 F.3d 71, 80 (5th Cir. 2011). A judge "abuses his discretion in denying recusal where `a reasonable man, cognizant of the relevant circumstances surrounding [the] judge's failure to recuse, would harbor legitimate doubts about that judge's impartiality.'" Id. (citation omitted).

We do not have any doubts about the district court's impartiality based on the instances of bias Jacqueline alleges. The limitation on Jacqueline's testimony was consistent with limits the judge placed on witnesses called by both sides, and the extension of the time limit from counsel's original estimate of 85 minutes to 110 minutes refutes any inference of impartiality. The decision to detain Jacqueline after conviction is a common one because of the presumption in favor of detention that attaches to a convicted defendant. See 18 U.S.C. § 3143. And the district court's decision to release Jacqueline a few weeks later based on the magistrate's recommendation again rejects any notion that the judge was out to get her. The supposed "investigation" into AuditGuard amounts to nothing more than the district court's asking a couple of benign questions about that other business of the Morrisons in another case.8 The district court's comments about Jacqueline's scheduled surgery involved the district court sensibly telling her to schedule the procedure prior to sentencing and came after Jacqueline had cited the surgery on multiple occasions as a basis for continuance. Similarly, the argument that the district court denied Jacqueline her counsel of choice misstates the record; the court simply denied improper motions for pro hac vice admission but admitted the attorney once a proper motion was submitted.

Alone or taken together, these circumstances do not rise to the level at which recusal is required. Adverse trial rulings, and much of what Jacqueline complains about does not even rise to that level, do not establish bias.9 United States v. MMR Corp., 954 F.2d 1040, 1045 (5th Cir. 1992).

C

Gladstone challenges different conduct of the trial judge. After the government presented two witnesses to show that the wire transfer from Express Tax to the Morrisons crossed state lines, the judge told the prosecutor the following outside the presence of the jury: "I don't think you have the evidence of what bank made the transfer ... in other words to get interstate commerce." Despite responding that he had shown the origin of the transfer (Kansas City), on rebuttal the prosecutor recalled one of the witnesses to clarify that point.

Gladstone contends that this exchange about the interstate wire element shows that the judge stepped into the shoes of the prosecutor. Because he did not raise an objection at trial, our review is for plain error. United States v. Bourgeois, 423 F.3d 501, 506 (5th Cir. 2005). We only have discretion to correct any error if Gladstone shows that the error is obvious, affected his substantial rights, and seriously affected the fairness and integrity of the district court proceedings. Id.

As we have already pointed out in discussing the use of time limits, a trial judge "has broad discretion in managing his docket, including trial procedure and the conduct of trial." Gray, 105 F.3d at 964 (quoting Sims v. ANR Freight System, Inc., 77 F.3d 846, 849 (5th Cir.1996)). "This discretion extends to commenting on the evidence, questioning witnesses to clarify facts or even elicit facts not yet presented, and moving along the trial by means of interruptions...." Id. A due process violation occurs "only if the judge so favors the prosecution that he appears to predispose the jury toward a finding of guilt or to take over the prosecutorial role." Derden v. McNeel, 978 F.2d 1453, 1459 (5th Cir. 1992) (citations omitted).

The concern about giving the jury the impression that the judge has an opinion as to guilt or innocence is not present here because the comments were made outside the presence of the jury. In another sense, however, that context of the judge's comments make them look, even if inadvertently made, more like advice to a party on weaknesses in its case as opposed to an attempt to clarify testimony that may be confusing to the jury. Cf. United States v. Allen, 136 F.3d 137, 1998 WL 30039, at *1 (5th Cir. 1998) (per curiam) (citations omitted) (finding no error when the district court's actions were out of "concern for the relevancy of the evidence solicited, preservation of the jury's role as fact finder, and an antipathy to wasted trial time"); United States v. Bermea, 30 F.3d 1539, 1571 (5th Cir. 1994) (holding that active judicial questioning was not an abuse of discretion).

Given the unusual nature of this suggestion that the government provide additional evidence on a particular issue, it is not surprising that we are unable to find an analogous case in this circuit.10 Even assuming error, however, Gladstone has not convinced us that comment prejudiced him. The wire that was the subject of the judge's comments related only to count 15. Prior to the judicial intervention, an H&R Block representative testified that the Express Tax payment to the Morrisons originated from a bank located in Kansas City. A subsequent witness from the bank may have created the confusion the judge referenced; she testified that although the wire documentation showed that it was received in Fort Worth, it only showed that it was sent by Wachovia Bank without listing a location (though it does list the holder of the sending account as being located in Kansas City). In recalling the H&R Block representative — the only consequence the jury saw of the judge's comment — the government essentially reiterated testimony that had already been given. This is not enough for Gladstone to prove an effect on his substantial rights.

IV

Jacqueline asserts additional claims of error that we can more readily reject. She argues that the government committed a Brady violation in not disclosing potential impeachment evidence in the form of tax returns for the testifying clients, including returns showing Schedules Cs that they filed before using JMA.11 But she has not made a showing that any available prior returns were not disclosed. In fact, the record reveals that tax information dating as far back as 2000 was listed as exhibits. Although that included transcripts of the returns rather than the actual filings for the years before 2005, Jacqueline has not demonstrated either that the actual returns are in the possession of the government (indeed, her trial counsel appeared to recognize that only transcripts were available for the oldest returns) or that the transcripts omit any potentially material information.

Her argument on this point may be more properly viewed as one challenging the late production of impeachment evidence. Because even the Department of Justice does not have direct access to tax returns, the parties had to file an agreed motion for a court order authorizing the IRS disclosure. Jacqueline's counsel filed that motion less than two weeks before trial, and received the information the Friday before trial started. Even when allegedly produced late in the course of a prosecution, Brady evidence can no longer be deemed to be "suppressed." United States v. McKinney, 758 F.2d 1036, 1049-50 (5th Cir. 1985). In such a situation, the analysis instead turns on whether the defendant was prejudiced by the tardy disclosure. Id. Even assuming production three days before trial qualifies as "late,"12 Jacqueline fails to show how she was prejudiced by the timing of the disclosure. The transcripts of old tax return information for multiple clients were introduced at trial.13

Jacqueline also sees error in the district court's refusal to include a civil IRS regulation relating to tax preparers in the jury instruction for her section 7206(2) counts.14 She contends the regulation would inform the jury of her legal duty as a tax preparer and demonstrate her good faith reliance on her understanding of the law. Although it denied the request to include the regulation in the jury charge, the district court told Jacqueline she could introduce it into evidence, which would also allow it to be discussed during closing argument.

We see no abuse of discretion in refusing the instruction. This court reviews challenges to jury instructions and refusals to give jury instructions for abuse of discretion. United States v. Monroe, 178 F.3d 304, 307 (5th Cir. 1999). A refusal to give a requested instruction constitutes reversible error only if, among other things, the charge given to the jury did not substantially cover the content of the proposed instruction. Id. That is not the case here because the pattern "willfulness" instruction the court gave — that a jury should only find Jacqueline guilty if she intended to violate the law — substantially covered the same ground as the additional instruction Jacqueline requested. 5TH CIRCUIT PATTERN INSTRUCTIONS (CRIMINAL) § 2.102A, B (explaining that the pattern instruction on willfulness is consistent with Cheek v. United States, 498 U.S. 192, 111 S.Ct. 604, 112 L.Ed.2d 617 (1991)).

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The judgment of the district court is AFFIRMED.