
561 F.3d 1150 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Kathryn V. ERICKSON, Defendant-Appellant,
United States of America, Plaintiff-Appellee,
v.
Gilman Ned Mitchell, Defendant-Appellant.
Nos. 08-4025, 08-4028.
United States Court of Appeals, Tenth Circuit.
April 6, 2009.
*1155 Edwin S. Wall of Edwin S. Wall, P.C., Salt Lake City, UT, for Defendant-Appellant, Kathryn V. Erickson.
Elizabethanne C. Stevens, Assistant United States Attorney, (Brett L. Tolman, United States Attorney, with her on the briefs), for Plaintiff-Appellee.
Submitted on the briefs: Loren E. Weiss, Stephen K. Christiansen, and Mary Jane E. Wagg, of Van Cott, Bagley, Cornwall & McCarthy, P.C., Salt Lake City, UT, for Defendant-Appellant Gilman Ned Mitchell.
Brett L. Tolman, United States Atttorney, and Elizabethanne C. Stevens, Assistant United States Attorney, Salt Lake City, UT, for Plaintiff-Appellee.
Before HENRY, Chief Circuit Judge, HARTZ, and O'BRIEN, Circuit Judges.
HARTZ, Circuit Judge.
Defendants Kathryn V. Erickson and Gilman N. Mitchell were each convicted on three counts of obstructing and impeding a federal grand jury. See 18 U.S.C. § 1503. The charges stemmed from the submission of backdated contract extensions (or "change orders") in response to a grand-jury subpoena for records of the Uintah Special Services District (USSD) in Uintah County, Utah. Ms. Erickson was USSD's general manager. The false change orders purported to extend three contracts to cover work by Mr. Mitchell's firm, Ned B. Mitchell Construction, Inc. (Mitchell Construction), after the contracts had expired.
On appeal Defendants contend that (1) the evidence was insufficient to support their convictions because the government did not establish that the false change orders interfered with the grand-jury investigation; (2) the government violated Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), by failing to disclose exculpatory audit documents; and (3) the bias of the trial judge deprived them of a fair trial. Ms. Erickson also contends that her trial counsel was ineffective. We have jurisdiction under 28 U.S.C. § 1291 and affirm the district court.

I. BACKGROUND
Ms. Erickson was the general manager of USSD, a political subdivision of the State of Utah created to use federal-mineral-lease revenues for road projects. She was USSD's only executive officer and administered its day-to-day affairs from a small office in Vernal, Utah. Authority to set USSD's policy, select bids, and award contracts lay with a three-person governing board appointed by the Uintah County Commission. Ms. Erickson prepared budgets for the board's approval, kept it informed of the status of USSD road projects, and submitted contractor invoices for board approval at its periodic meetings. She did not have personal authority to enter into or modify contracts for USSD or to expend more than $1,000 of USSD funds. Cheryl McCurdy was Ms. Erickson's secretary and maintained USSD's files.
Mitchell Construction was a major contractor for USSD. In 1998, USSD awarded Mitchell Construction a contract to haul gravel from a site called Hamaker Bottoms *1156 and another contract to carry out small asphalt-paving projects. Although the Hamaker Bottoms contract itself does not contain an expiration date, Mitchell Construction's bid for the contract, which is attached to the agreement, states that "[t]his will be a one-year agreement from January 1, 1998 to December 31, 1998." Supp. R. (Erickson & Mitchell) Vol. XV Ex. 6A at 5 ¶ 5. The small-paving-projects contract recites that the work contracted for will be completed within the 1998 construction year.
During 1999 and 2000 Mitchell Construction continued to perform work on the projects covered by its 1998 contracts with USSD, despite their expiration. It submitted invoices to USSD for this work, which Ms. Erickson presented to USSD's board. The board approved payment of the invoices in every instance, with two board members signing each check to Mitchell Construction.
In June 1999 the United States Department of Transportation's Office of the Inspector General began to investigate contracting irregularities at USSD and the Uintah County Road Department. This investigation was later consolidated with a parallel inquiry by the Federal Bureau of Investigation. Neither Ms. Erickson nor Mr. Mitchell was personally a target of the investigation at first, though Mitchell Construction's contracts with USSD were within the investigation's scope. In late 1999 the United States Attorney for the District of Utah opened a grand-jury investigation.
In January 2000 the grand jury issued a subpoena duces tecum to USSD. Among the documents covered by the subpoena were copies of USSD's "project contracts, invoices," and "any other documents relative to all transactions" between USSD and contractors. Id. Ex. 21 ¶ 15, 17. The following month Ms. Erickson and McCurdy compiled and photocopied a limited number of USSD records for the grand jury. In July 2000 the grand jury made a second request for USSD records covered by the subpoena. During the first week of August, Ms. Erickson and McCurdy again compiled and photocopied documents.
McCurdy testified at trial that while working on the response to the grand jury she saw Ms. Erickson prepare a handwritten change order for the Hamaker Bottoms contract and saw Ms. Erickson and Mr. Mitchell both sign it. The change order, which was backdated to January 13, 1999 (a short time after the original contract had expired), extended the contract through December 31, 2000.
McCurdy later discovered that two other change orders had been created and backdated. She testified that she spent the workday of August 3, 2000, compiling and photocopying USSD records for the second submission to the grand jury. Alone in the office the entire day, she recorded on a handwritten list the documents that she copied for the grand jury, as Ms. Erickson had instructed her. (This list included the Hamaker Bottoms backdated change order signed by Ms. Erickson and Mr. Mitchell a day or two earlier.) McCurdy left the office at 6:30 p.m. to eat dinner at home. She planned to return afterwards to meet Ms. Erickson for a final check of the documents, but Ms. Erickson called McCurdy at home and told her that the documents were in order, so there was no need for her to return to work that evening.
After the subpoenaed records were turned over to Bruce Reading, USSD's legal counsel, for delivery to the grand jury, McCurdy repeatedly asked Ms. Erickson to return her handwritten document list so that it could be filed, but without success. A week to ten days after the documents went to Reading, McCurdy found on Ms. Erickson's desk a photocopy *1157 of her list and a similar list in Ms. Erickson's handwriting. Suspecting that "irregularities... were going on," McCurdy examined the lists. R. Vol. IX Doc. 192 at 15. (Cites to "R." refer to record filed in 08-4025 (Erickson)). On the photocopy of her own list McCurdy saw that two entries not in her handwriting had been added. These entries were for change orders to the small-paving-projects contract between Mitchell Construction and USSD. McCurdy "knew [USSD's] files by heart" and believed that no such change orders had existed when she had compiled her list. Id. McCurdy also examined the list in Ms. Erickson's handwriting and noted that it resembled her own in its original form, except that it used different numbering and included the same two entries that had been added to her own list. McCurdy then looked in USSD's files for the documents reflected by these entries, eventually finding them with files for 1998. Both were signed by Ms. Erickson and Mr. Mitchell. The first change order, dated April 12, 1999, required work to be completed by December 31, 1999. The second change order was dated March 20, 2000, and set a completion date of December 31, 2000.
In 2005, after Ms. Erickson had been fired (in 2002), USSD asked Reading to return documents related to the grand-jury production. Among these was McCurdy's original handwritten list created on August 3, 2000. McCurdy saw that two entries had been added to her list.
Ms. Erickson and Mr. Mitchell were each indicted by a grand jury in the U.S. District Court for the District of Utah on three counts of violating 18 U.S.C. § 1503. Each count corresponded to a backdated change order and charged that Defendants had obstructed justice by knowingly falsifying a document with the knowledge and intent that the grand jury would rely on it.
Before trial both the prosecution and the defense asked the district court to limit the evidence to be presented to the jury regarding the subject matter of the grand-jury investigation. The government filed a motion in limine to exclude evidence that it had failed to charge Defendants with any substantive offenses; and Defendants objected to the government's notice of intent to introduce "background and historical evidence to allow the jury to understand the meaning of the three change orders in context." R. Vol. II Doc. 94 at 2 (internal quotation marks omitted). The court granted the government's motion; and in response to Defendants' objection to background evidence, it said that it would limit such evidence to what would be necessary to establish the elements of the offense. Nevertheless, saying that "the jury may and should be aware of the established fact of the existence of the investigation," id. at 5, the court asked the parties to prepare a stipulation on language to be read to the jury. In response the parties stipulated that the subpoena served on USSD had been duly issued by the grand jury and that, in compliance with the subpoena, Ms. Erickson had delivered documents to USSD's attorney, Bruce Reading, for delivery to the grand jury. But because the parties had not been able to stipulate to anything further, the court told them that it would have to deal with the issue as it arose at trial and warned: "If the government does present evidence as to the nature and extent of the investigation, then the Court will have to allow [Defendants] to provide evidence that no additional indictments were filed." Id. Vol. VII Doc. 190 at 136-37.
The trial took five days. On January 26, 2007, the jury returned a verdict of guilty against both Defendants on all three counts. On February 6 counsel for Ms. Erickson and Mr. Mitchell moved for a judgment of acquittal or, in the alternative, *1158 a new trial. They contended that the evidence was insufficient to support their convictions and that comments by the court in the jury's presence biased the jury against Defendants. In June counsel supplemented the motion with citations to the trial transcript and legal authorities. The following month Ms. Erickson filed a pro se motion for acquittal or, in the alternative, a new trial. She contended that her trial counsel had been ineffective and that she had been denied a fair trial because evidence favorable to her had been kept from the jury by the district court's evidentiary rulings, by her counsel's inattention, and, to some extent, by the government's actions.
The district court denied Defendants' motions. With regard to the sufficiency of the evidence, the court held that the jury could reasonably infer that Ms. Erickson and Mr. Mitchell created false, backdated documents with the specific intent to obstruct justice. The court rejected Defendants' bias argument, explaining that its comments had been aimed at proper courtroom administration and that they did not suggest a belief in the Defendants' guilt. The court also held that Ms. Erickson's pro se motion was untimely and that, in any event, it was largely an "attempt[ ] to retry the case." Id. Vol. III Doc. 155 at 10.
In January 2008 the district court sentenced each Defendant to 30 months' probation. Shortly thereafter, Defendants again moved for a new trial, this time alleging that the government had violated Brady by withholding two items. The first item was a "limited forensic examination" of USSD's paving and hauling contracts. Id. Doc. 168 at 2-3. The examination had been conducted by Robert Foley, a certified public accountant who was USSD's regular outside auditor. According to Defendants, this examination had found "no impropriety by Mr. Mitchell or his company." Id. at 3.
The second item was an audit memorandum by Foley concerning the Hamaker Bottoms contract. The memorandum, denoted Exhibit 4-B, reports that McCurdy told Foley that she had found the change order for this contract in USSD's office and does not suggest that she had seen Defendants create and sign it. Defendants argued that Foley's version of McCurdy's story contradicted her trial testimony and could have been used to impeach her.
The district court denied the motion, ruling that the forensic examination was not material evidence under Brady and that Exhibit 4-B had been available to Defendants before trial.

II. DISCUSSION
Ms. Erickson and Mr. Mitchell challenge the sufficiency of the evidence to sustain their convictions, the district court's rejection of their Brady challenges, and the court's ruling on bias. Ms. Erickson also contends that her trial counsel rendered ineffective assistance, in violation of her Sixth Amendment rights.

A. Sufficiency of the Evidence
"[I]n reviewing the sufficiency of the evidence to support a jury verdict, this court must review the record de novo and ask only whether taking the evidence  both direct and circumstantial, together with the reasonable inferences to be drawn therefrom  in the light most favorable to the government, a reasonable jury could find the defendant guilty beyond a reasonable doubt." United States v. Hanzlicek, 187 F.3d 1228, 1239 (10th Cir.1999) (internal quotation marks omitted). "While the evidence supporting the conviction must be substantial and do more than raise a mere suspicion of guilt, it need not conclusively *1159 exclude every other reasonable hypothesis and it need not negate all possibilities except guilt." United States v. Burkley, 513 F.3d 1183, 1188 (10th Cir.2008) (brackets and internal quotation marks omitted).
The Defendants were convicted of violating 18 U.S.C. § 1503, which prohibits "corruptly ... influenc[ing], obstruct[ing], or imped[ing], or endeavor[ing] to influence, obstruct, or impede, the due administration of justice." We have identified three "core" elements of this offense: "(1) there must be a pending judicial proceeding; (2) the defendant must have knowledge or notice of the pending proceeding; and (3) the defendant must have acted corruptly with the specific intent to obstruct or impede the proceeding in its due administration of justice." United States v. Wood, 6 F.3d 692, 695 (10th Cir.1993) (internal quotation marks omitted). In construing the elements of the offense, the Supreme Court has endorsed a nexus test, requiring that
[t]he action taken by the accused must be with an intent to influence judicial or grand jury proceedings; it is not enough that there be an intent to influence some ancillary proceeding, such as an investigation independent of the court's or grand jury's authority.... [T]he act must have a relationship in time, causation, or logic with the judicial proceedings. In other words, the endeavor must have the natural and probable effect of interfering with the due administration of justice.... [I]f the defendant lacks knowledge that his actions are likely to affect the judicial proceeding, he lacks the requisite intent to obstruct.
United States v. Aguilar, 515 U.S. 593, 599, 115 S.Ct. 2357, 132 L.Ed.2d 520 (1995) (citations and internal quotation marks omitted). "The nexus limitation is best understood as an articulation of the proof of wrongful intent that will satisfy the mens rea requirement of `corruptly' obstructing or endeavoring to obstruct." United States v. Quattrone, 441 F.3d 153, 170 (2d Cir.2006).
Ms. Erickson and Mr. Mitchell concede that the first two elements of the offense are not at issue: a grand-jury proceeding was pending at the time of the charged conduct and both Defendants knew of it. Moreover, although Defendants' briefs occasionally speak in general terms of the absence of evidence of intent, their specific arguments focus on the issue of nexus. (They do not address, for example, the evidence regarding their hostility to the grand-jury investigation or their concern about their own exposure.) The essence of their various arguments is that the government failed to show how their conduct affected the grand-jury investigation.
We are not persuaded. Indeed, the Supreme Court opinion adopting the nexus requirement described a circumstance very much like the one before us to exemplify how the nexus requirement could be satisfied. Aguilar distinguished the conduct of the defendant in that case  lying to FBI agents who were not acting as an arm of the grand jury and had not been summoned to testify before it  from that of a defendant who submits false documents to the grand jury itself:
[T]he evidence goes no further than showing that [the defendant] testified falsely to an investigating agent. Such conduct, we believe, falls on the other side of the statutory line from that of one who delivers false documents or testimony to the grand jury itself. Conduct of the latter sort all but assures that the grand jury will consider the material in its deliberations.
515 U.S. at 601, 115 S.Ct. 2357. As the Second Circuit has said:
A defendant's awareness that a subpoena seeks documents, coupled with his actions taken to place those documents *1160 beyond the grand jury's reach clearly would meet the ... nexus requirement.... [I]t is enough if he knows that a subpoena calls for a category of documents, or even one particular document, and then takes steps to place those documents beyond the reach of the grand jury.
Quattrone, 441 F.3d at 171; see also United States v. Rasheed, 663 F.2d 843, 852 (9th Cir.1981) ("the [petit] jury must find that ... knowing that the particular documents were covered by the subpoena, [the defendant] willfully concealed or endeavored to conceal them from the grand jury"). Here, the Defendants created false documents to deliver to the grand jury in response to its subpoena. The evidence was sufficient to satisfy the nexus requirement.
Defendants' arguments to the contrary are unpersuasive. Both Defendants insist that the government failed to present evidence that the grand jury was misled or otherwise affected by their submission of falsified change orders. But the required nexus is only that the charged conduct "have the natural and probable effect of interfering with the due administration of justice." Aguilar, 515 U.S. at 599, 115 S.Ct. 2357 (internal quotation marks omitted). Success is not necessary; "an `endeavor' suffices." Id.
Ms. Erickson also asserts that the backdated change orders did no more than memorialize the reality of what had happened during 1999 and 2000; that reality, she says, was that Mitchell Construction continued to do work for USSD and to submit invoices that its board duly paid. But a reasonable jury could reject this innocent explanation for the change orders. USSD board member Merlin Sinfield testified that the board trusted Ms. Erickson and did not scrutinize the paperwork she presented to it, which typically included multiple invoices for each check. Sinfield also testified that the board had not known of the change orders and that he now recognized that it was improper for USSD to pay Mitchell Construction after the Hamaker Bottoms and small-paving contracts had run. In any event, the fraudulent documents compromised the grand jury's ability to make its own determination whether the work in 1999 and 2000 was authorized. A grand jury is obstructed whenever it is presented with manufactured evidence, even if the manufacturer thinks that the evidence supports "reality." Ms. Erickson's challenge to the sufficiency of the evidence on this ground fails.
Ms. Erickson further contends that the requirement of § 1503 that she acted "corruptly" was not satisfied because "[t]here is no evidence the change orders resulted in any advantage to anyone, influenced any witness or had any impact with the official duties or rights of anyone." Erickson Aplt. Br. at 33. She draws her argument from United States v. Ogle, 613 F.2d 233 (10th Cir.1979), in which the definition of corruption that we quoted from a legal dictionary included, "`An act done with an intent to give some advantage inconsistent with official duty and the rights of others.'" Id. at 238 (quoting Bouvier's Law Dictionary). But another part of the quoted definition was, "`Something against law.'" Id. And we "approve[d] fully" the district court's view that "an endeavor to influence a juror in the performance of his or her duty or to influence, obstruct or impede the due administration of justice is per se unlawful and is tantamount to doing the act corruptly." Id. In other words, an act is done "`corruptly'" when "done with the purpose of obstructing justice." Rasheed, 663 F.2d at 852. Thus, the proof in this case of intent to obstruct necessarily established corrupt intent.
*1161 Finally, Mr. Mitchell argues that relevance to the grand-jury investigation is an element of obstruction under § 1503, and he contends that the falsified change orders were not relevant and that the district court improperly excluded background evidence that would have shown the irrelevance. We disagree. To begin with, there is no real question of relevance in this case. A federal grand jury has broad inquisitorial powers. As the Supreme Court has explained:
The grand jury occupies a unique role in our criminal justice system. It is an investigatory body charged with the responsibility of determining whether or not a crime has been committed. Unlike this Court, whose jurisdiction is predicated on a specific case or controversy, the grand jury can investigate merely on suspicion that the law is being violated, or even just because it wants assurance that it is not. The function of the grand jury is to inquire into all information that might possibly bear on its investigation until it has identified an offense or has satisfied itself that none has occurred. As a necessary consequence of its investigatory function, the grand jury paints with a broad brush. A grand jury investigation is not fully carried out until every available clue has been run down and all witnesses examined in every proper way to find if a crime has been committed.
United States v. R. Enterprises, Inc., 498 U.S. 292, 297, 111 S.Ct. 722, 112 L.Ed.2d 795 (1991) (citations and internal quotation marks omitted). Accordingly, a grand-jury subpoena is invalid for lack of relevance only if "there is no reasonable possibility that the category of materials the Government seeks will produce information relevant to the general subject of the grand jury's investigation." Id. at 301, 111 S.Ct. 722. Defendants have not suggested the existence of any evidence that was admitted at trial, or that could have been presented to the district court, that would have shown no such reasonable possibility. See id. at 301-02, 111 S.Ct. 722 (burden is on party opposing grand-jury subpoena to overcome presumption of relevance).
Moreover, even if the subpoenaed documents were not within a category of relevant records, one who falsifies documents provided in response to a subpoena may well be "endeavor[ing] to influence, obstruct, or impede" the grand jury. 18 U.S.C. § 1503(a). Indeed, it is difficult to imagine why one would falsify documents to be presented to a grand jury if one did not believe that the documents were relevant to the grand jury's investigation (and would affect that investigation). We see no policy reason to protect a defendant from prosecution under § 1503 just because he or she misjudged the scope or purpose of the grand jury's investigation and submitted fraudulent information that could not have affected the actual investigation. As previously noted, "an `endeavor' suffices." Aguilar, 515 U.S. at 599, 115 S.Ct. 2357. One might argue that if the fraudulent documents were irrelevant to the grand jury's investigation, it would have been impossible to influence or impede the investigation by submitting the documents. But "impossibility" is not a defense under § 1503. See Osborn v. United States, 385 U.S. 323, 333, 87 S.Ct. 429, 17 L.Ed.2d 394 (1966). But cf. Aguilar, 515 U.S. at 610 n. 1, 115 S.Ct. 2357 (Scalia, J., concurring in part and dissenting in part) ("impossibility" defense may be available when there is no pending judicial proceeding).
Thus, we agree with the Sixth Circuit's holding that "the government need not prove, as an element of [§ 1503], that... alterations [of documents] made in response to a grand jury subpoena were relevant to the grand jury's investigation." United States v. Mullins, 22 F.3d 1365, *1162 1370 (6th Cir.1994). Mullins arose from a grand-jury investigation of the Detroit Police Department's use of a "`secret service fund.'" Id. at 1367. The grand jury subpoenaed the flight logs of officers in the department's aviation section, including that of Mullins. Mullins told fellow officers to delete flights to "questionable" destinations such as Las Vegas before turning over their logs, and he altered his own log. Id. He was later convicted of violating § 1503. The Sixth Circuit rejected Mullins's argument that because the grand jury's focus was not aviation-section abuses, his conduct had no "`reasonable relationship'" to the investigation. Id. at 1369. It explained:
[T]he evidence conclusively showed that what Mullins did, he did in response to the grand jury's subpoena. The alterations Mullins made and ordered were intended to deprive the grand jury of evidence that it had decided was relevant to its investigation. There is no authority requiring this court to second-guess the scope of the grand jury's investigation... simply because the abuses Mullins now contends he sought to hide may not have been precisely the abuses that he asserts the grand jury sought to expose.
Id. at 1370.
We recognize that there is language supporting Mr. Mitchell's relevance argument in the Ninth Circuit's opinion in United States v. Ryan, 455 F.2d 728 (9th Cir. 1971). But to the extent that Ryan requires the government to prove that subpoenaed documents were relevant to the grand-jury investigation, we simply disagree, for the reasons stated above. In any event, the result in Ryan may be defended on a narrower ground. The thrust of the opinion is that the IRS had improperly commandeered a grand jury's subpoena power for its own purposes. See id. at 730-32, 734-35. As the Sixth Circuit has said, "The issue in Ryan, we believe, was whether the investigation was being conducted by the IRS, in which case § 1503 did not apply, or by the grand jury." Mullins, 22 F.3d at 1370. There is no evidence, or even a suggestion, of such misuse of a grand jury in this case. Therefore, we need not decide whether we would embrace the result in Ryan based on this narrower theory.
In brief, we hold that knowingly submitting fraudulent documents in response to a grand-jury subpoena constitutes obstruction of justice, when, as here, a grand-jury proceeding is underway and the defendant knows of it. The evidence was therefore sufficient to convict Defendants of violating § 1503.

B. Brady Challenges
In Brady the Supreme Court held that "the suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment." 373 U.S. at 87, 83 S.Ct. 1194. Brady's holding has since been extended to require disclosure by the prosecutor even when the defendant has not requested the withheld material or has made only a general request, see United States v. Agurs, 427 U.S. 97, 107, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976), and to cover impeachment evidence as well as exculpatory evidence, see United States v. Bagley, 473 U.S. 667, 676, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985).
Defendants contend that the government violated the Brady doctrine by failing to disclose what they term a "limited forensic examination" by Robert Foley, USSD's outside auditor, of USSD's paving and hauling contracts with Mitchell Construction. Erickson Aplt. Br. at 35. Mr. Mitchell also contends that the government was required to disclose a document denoted Exhibit 4-B, an audit memorandum *1163 written by Foley concerning the Hamaker Bottoms contract. The district court denied Defendants' January 2008 motion for a new trial based on these alleged nondisclosures.
To establish a Brady violation, the defendant must prove that the prosecution suppressed evidence, the evidence was favorable to the defense, and the evidence was material. See United States v. DeLuna, 10 F.3d 1529, 1534 (10th Cir. 1993). A Brady claim fails if the existence of favorable evidence is merely suspected. That the evidence exists must be established by the defendant. See United States v. Lopez, 372 F.3d 1207, 1209-11 (10th Cir.2004) (because defendant failed to establish that government had promised leniency to prosecution witnesses, there could be no Brady violation in government's failure to turn over documentation of such promises); United States v. Warren, 454 F.3d 752, 759 (7th Cir.2006) (defendant failed to establish existence of any document withheld by government, so "his Brady claim fails to get off the ground."). And the defendant must also show that the favorable evidence was in the possession or control of the government. See United States v. Gardner, 244 F.3d 784, 788 (10th Cir.2001); Coe v. Bell, 161 F.3d 320, 344 (6th Cir.1998) ("Brady obviously does not apply to information that is not wholly within the control of the prosecution."); United States v. Maldonado-Rivera, 489 F.3d 60, 67 (1st Cir.2007) ("For Brady to operate, the government not only must know about undisclosed evidence but also must have custody or control of that evidence."). The prosecutor herself need not have, or even know of, the evidence if one of her agents has it. See United States v. Velarde, 485 F.3d 553, 559 (10th Cir.2007) (defendant can base a Brady claim on government investigator's failure to disclose even when prosecutor is ignorant of the evidence). Furthermore, a defendant is not denied due process by the government's nondisclosure of evidence if the defendant knew of the evidence anyway. See Spears v. Mullin, 343 F.3d 1215, 1256 (10th Cir.2003) ("[T]here can be no suppression by the state of evidence already known by and available to the defendant prior to trial.") (brackets and internal quotation marks omitted); United States v. Quintanilla, 193 F.3d 1139, 1149 (10th Cir. 1999) ("If a defendant already has a particular piece of evidence, the prosecution's disclosure of that evidence is considered cumulative, rendering the suppressed evidence immaterial."); Coe, 161 F.3d at 344 (no Brady violation is possible when defendant "knew or should have known the essential facts permitting him to take advantage of any exculpatory information" or when the evidence is available to him from another source, such as a witness "to whom he had as much access as the police." (internal quotation marks omitted)).
"While we ordinarily review a district court's denial of a motion for a new trial for an abuse of discretion, when the motion is based on an alleged Brady violation, we review the district court's decision de novo." United States v. LaVallee, 439 F.3d 670, 698 (10th Cir.2006). To the extent that the Brady analysis turns on historical fact, however, we accept the fact finding of the district court unless clearly erroneous. See Lopez, 372 F.3d at 1210. We can affirm on a ground not relied upon by the district court if the record requires affirmance on that ground and it is not unfair to the appellant to rely on that ground. See Maldonado v. City of Altus, 433 F.3d 1294, 1302-03 (10th Cir.2006), overruled on other grounds by Burlington N. & Santa Fe Ry. Co. v. White, 548 U.S. 53, 126 S.Ct. 2405, 165 L.Ed.2d 345 (2006). We hold that Defendants have failed to show a Brady violation.
We first address the "forensic examination" by auditor Foley. To establish *1164 the existence of this examination, Defendants point to the minutes of the December 28, 1999, meeting of the Uintah County Commission. The minutes reflect that Foley's firm was hired at that meeting to conduct an audit. According to the minutes:
[The audit would be] looking to see if all the reimbursements are appropriate that are received from the state and reimbursements from the Special Service District to the Road Department, that they are allocated to the right places, and that all the billings from the Road Department to special service district is correct and that when the money comes back into the clerk-auditors office that it is accounted for in the appropriate account.
[The audit would also] review contracts for the services regarding asphalt and gravel between vendors and Uintah County.
Commissioner Swain questioned between the Special Service District also?
Commissioner Harrison said yes, and it will move into the asphalt areas.
R. Vol. III Doc. 168-4 at 4 (full capitalization omitted).
Defendants have not shown, however, that the government obtained a copy of the audit or otherwise knew of its contents. Although they correctly point out that FBI Agent Rex Ashdown attended the December 28 meeting at which the audit was apparently ordered, they have presented no evidence that Ashdown obtained the audit or learned of its conclusions.
In addition, Defendants have failed to show that the audit contained any material evidence favorable to them. We cannot discern from the meeting minutes (or anything else in the record) whether the audit encompassed the contracts or the change orders of interest in this case. Defendants' only "evidence" of the contents of the audit is a letter from a former Uintah County commissioner to defense counsel, which states that the audit "showed absolutely no improprieties." R. Vol. III Doc. 168-2 at 2. (The letter also states that FBI Agent Ashdown was aware of the audit but it does not assert that he knew the results of the audit, or how the letter's author had personal knowledge of Ashdown's awareness.)[1] But the letter is unsworn and therefore cannot support a motion for a new trial under Brady. See Velarde, 485 F.3d at 560 (defendant is not even entitled to evidentiary hearing on new-trial motion brought under Brady unless defendant presents admissible evidence that would, if believed, warrant relief). We note that Defendants did not seek additional discovery, or even an evidentiary hearing, to support their Brady claim. See id. at 559-60. Thus, Defendants have failed to show that the government controlled or possessed the findings of the "limited forensic examination" or that the examination provided material, favorable information. Because the government argued in district court this ground for rejecting the Brady claim, it is fair to affirm on this ground even though the district court did not rely on it. See Maldonado, 433 F.3d at 1302-03.
The second Brady challenge is raised on appeal only by Mr. Mitchell. We reject his challenge because the district court did not clearly err in finding that he had been aware of and had access to Exhibit 4-B before trial.
Exhibit 4-B was an audit memorandum written by CPA Foley regarding the Hamaker Bottoms contract. It reports what McCurdy told him regarding her discovery *1165 of the change order. Mr. Mitchell contends that it would have assisted his defense because it contains no mention that she saw Ms. Erickson prepare the change order or saw Ms. Erickson and Mr. Mitchell sign it, which was her testimony at trial.
The district court rejected this Brady claim on the ground that the exhibit was available to Mr. Mitchell by the time of trial. As we have stated, if the defendant had the evidence at trial, he has no Brady claim. See Quintanilla, 193 F.3d at 1149. The court relied on Ms. Erickson's pro se motion for a new trial, which attached Exhibit 4-B. Although Ms. Erickson repeatedly asserts in her motion that evidence favorable to her was "withheld," she uses that term to include evidence that the district court ruled inadmissible and evidence known to her attorney but not used at trial. The motion complains that some evidence was "withheld" by the prosecution and investigators, but Exhibit 4-B is not among the items that she alleges to have been so withheld. Her comments regarding the contents of the exhibit never include an assertion that the document had only recently come to her attention. To the contrary, she says that most of the evidence discussed in her motion "is not `new' evidence." R. Vol. III Doc. 132 at 14. Mr. Mitchell's brief on appeal contains no argument disputing that Ms. Erickson had Exhibit 4-B by the time of trial.
Furthermore, the record contains additional evidence that virtually compels the district court's finding. Mr. Mitchell acknowledges that Exhibit 4-B is discussed at length in an April 2001 letter to Foley from Mr. Mitchell's lawyer at the time, Bruce Reading. The end of the letter recites "cc: Gil Mitchell." United States v. Mitchell, No. 2:05-CR-00521-TS (Position Statement Regarding the Presentence Investigation Report & Sentencing Mem., Ex. A at 10 (Dec. 21, 2007)). Mr. Mitchell suggests that the letter is unimportant because "the fact that the letter discusses Exhibit 4-B does not mean the government produced Exhibit 4-B as required by Brady." Mitchell Reply Br. at 7. But he is mistaken. To repeat, a defendant is not deprived of due process by the government's failure to disclose information if the defendant has obtained the information through other means. See Spears, 343 F.3d at 1256; Coe, 161 F.3d at 344.
We also note that the prosecutor represented to the district court that Exhibit 4-B was among documents in the open-file discovery available to Defendants before trial. Such representations are entitled to almost as much weight as an affidavit. As we have explained:
To reject the [federal prosecutor]'s representation is not only to ignore "the presumption of regularity" ... but to disregard the [prosecutor]'s duty as an attorney. "Attorneys are officers of the court, and when they address the judge solemnly upon a matter before the court, their declarations are virtually made under oath."
United States v. Deberry, 430 F.3d 1294, 1300 (10th Cir.2005) (quoting Holloway v. Arkansas, 435 U.S. 475, 486, 98 S.Ct. 1173, 55 L.Ed.2d 426 (1978)).[2]
*1166 In sum, Mr. Mitchell has not shown that the district court clearly erred when it determined that he had known of and had access to Exhibit 4-B before trial. Accordingly, his Brady claim with respect to this piece of evidence fails.

C. Alleged Bias by the District Court
Defendants contend that the district court's bias requires reversal of their convictions. The district court rejected the claim, ruling that its comments during trial had been aimed at courtroom administration and did not suggest a belief in the Defendants' guilt.
Defendants appear to be presenting two types of bias claims: (1) the judge deprived Defendants of a fair trial by conveying to the jury that he favored the prosecution, and (2) the judge should have recused himself because "his impartiality might reasonably [have] be[en] questioned," 28 U.S.C. § 455. See United States v. Donato, 99 F.3d 426, 434 (D.C.Cir.1996) (per curiam) (distinguishing "statutory case[s], where the claim [i]s that the trial judge should have recused himself" under § 455, from cases in which the defendant "claims that the district court judge displayed such bias against her and her attorney that she did not receive a fair trial."). It is often unclear in Defendants' appellate briefs which claim is being argued when a particular event or ruling is discussed. We need not decide precisely what claims are being raised, however, because we find no reversible error even if we apply both theories to all the relevant conduct complained of.
We begin with the claim that the trial judge conveyed to the jury that he favored the prosecution. When presented with such a claim,
our task is not to determine whether the trial judge's conduct left something to be desired, or even whether some comments would have been better left unsaid, but rather to determine whether the judge's behavior was so prejudicial that it denied [the defendant] a fair, as opposed to perfect, trial. Thus we examine the record to determine if jurors have been impressed with the trial judge's partiality to one side to the point that this became a factor in their determination.
United States v. Deters, 184 F.3d 1253, 1256 (10th Cir.1999) (citation, brackets, and internal quotation marks omitted); see United States v. Pisani, 773 F.2d 397, 402 (2d Cir.1985) (defining the inquiry as "whether the trial judge's conduct has improperly tipped the balance of the trial against the defendant.").
We are unpersuaded that any statements by the trial judge in the jury's presence would have suggested to the jury that the judge favored the prosecution. We review the statements individually, but even considered cumulatively they display no favoritism and did not deprive Defendants of a fair trial.
First, Defendants complain of the following question asked of the jury panel at voir dire:
If you were to serve as a juror in this case, would you be affected in any way if evidence is presented during the course of this trial that showed that these defendants were investigated for other possible crimes or criminal activity but that no indictments were returned regarding such crimes or criminal activity? Specifically would such evidence of other matters being investigated lead you to believe that because they were investigated for crimes not alleged in the indictment, that they were guilty of the crimes alleged in the indictment or that they are not guilty of the crimes alleged in the indictment because they were not indicted for other crimes investigated?
*1167 R. Vol. VII Doc. 190 at 92-93. This question strikes us as perfectly neutral. It hardly suggests that the judge believed that Defendants were more likely to be guilty because they had been investigated.
Defendants' second complaint concerns the judge's scolding of Ms. Erickson's attorney for speaking too fast during closing argument. At one point the judge said "[S]low down. If I have to tell you again, I am going to put a finger in front of you and go like this and let you speak to it." Id. Vol. XI Doc. 194 at 615. But the judge made clear that his motive was not hostility toward counsel but concern that the court reporter could not take down everything that was being said. And Defendants do not dispute that counsel was in fact speaking too fast. Indeed, after being chastised the first time by the judge, counsel responded: "I'll try and slow down. That's always been a problem for me. I had a high school teacher yell at me that if I wanted to be a lawyer, I better learn to slow down. I never did listen to him." Id. at 597. We have no doubt that the jury would not have perceived the judge's warnings as showing any bias against Defendants.
Third, Defendants complain of occasions during closing argument when the judge sustained objections to defense counsels' statements on the ground that they were asserting facts not supported by the evidence at trial. Defendants do not challenge the propriety of sustaining the objections and, in any event, such a challenge would fail. Rather, they focus on what the judge said in making the rulings. One comment to the jury that they challenge was: "[M]y view of the evidence and Mr. Weiss's view of the evidence is not what counts, it is your view of the evidence." R. Vol. XI Doc. 194 at 629. They fault the statement for saying that only the views of the judge and Mr. Weiss (counsel for Mr. Mitchell) did not countomitting any reference to the prosecutor's view and thereby indicating "that what the prosecutor said did count," Erickson Aplt. Br. at 46. We doubt that a juror would so interpret the remark. Surely Defendants would not suggest that the judge was implying that the views of Ms. Erickson's attorney (who, like the prosecutor, was not explicitly mentioned by the judge) "counted." A second challenge has more substance. In sustaining the prosecutor's objection to a statement by Mr. Mitchell's attorney, the court said to the jury: "Ladies and gentlemen, disregard what Mr. Weiss has just said. There is no evidence. Very inappropriate, Mr. Weiss." R. Vol. XI Doc. 194 at 637. Perhaps this language suggested anger, or at least impatience, with Mr. Weiss; but we can presume that jurors are capable of distinguishing between a judge's view of particular behavior by counsel and the judge's view of the merits of the case. See United States v. DiTommaso, 817 F.2d 201, 220 (2d Cir. 1987), ("[R]eversal is not mandated where... rebukes of defense counsel reflected not upon the merits of the case but rather on the way it was being handled.").
Moreover, the judge's chastising of counsel during trial was not one-sided. On three occasions during the prosecutor's examination of witnesses (twice without prompting by a defense objection), the court instructed the prosecutor not to "testify" when asking questions. R. Vol. IX Doc. 192 at 163, 266; Id. Vol. XI Doc. 194 at 520. And during the prosecutor's closing argument the court sustained a defense objection that the prosecutor had mischaracterized an argument made by Mr. Mitchell's counsel, saying, "The point Mr. Weiss is making, however, is ... you just represented something he said. I agree, he did not say what you just represented." Id. at 648.
*1168 Finally, Defendants complain of comments by the judge regarding their "opening the door" by asking certain questions. On the first occasion, after defense counsel had elicited from CPA Foley that his audit of USSD for 1999 had not uncovered irregularities, the prosecutor said: "Your Honor, it's going to be our position now that the door has been opened into the other areas," and the judge responded "I would agree." Id. Vol. X Doc. 193 at 419-20. On the second occasion, after Wendy Lewis, defense counsel for Ms. Erickson, asked USSD attorney Reading whether he had had "conversations ... regarding whether or not Mr. Mitchell or Ms. Erickson were targets of the grand jury investigation," the prosecutor said, "Your Honor, I object," and the judge responded, "Ms. Lewis, if you prevail in this question you will be opening a door that will be swung far wider than you want." Id. at 470.
We fail to see how the judge's statement on the first occasion would convey to the jury any bias in favor of the prosecution. As for the second statement, Defendants argue that the judge's comment suggested that they had something to hide and were trying to conceal evidence from the jury. Although we doubt that the judge's comment conveyed to the jury that he favored the government, Defendants' complaint has some force and we address on the merits whether the comment denied them a fair trial. In our view, it would have been better practice if the judge had saved the comment for a bench conference. But there was nothing extraordinary here that would require a new trial. Whenever an attorney objects to evidence, the jury could infer that the attorney has something to hide. Without disregarding the potential impact of the judge's comment, we note that in this instance it was the prosecutor who objected, which signaled to the jury that he did not want the question answeredthat is, he was trying to hide something. Because the risk of improper jury inferences from objections by counsel and rulings by the court is inherent in any trial, it is customary for the court to instruct the jury on the matter at the outset of trial. The district court did so here, saying:
Certain things are not evidence and must not be considered by you. I will list them now.
First, statements, arguments and questions by lawyers are not evidence.
Second, objections to questions are not evidence. Lawyers have an obligation to their clients to make an objection when they believe evidence being offered is improper under the rules of evidence. You should not be influenced by the objection or the Court's ruling on it. If the objection is sustained, ignore the question. If it is overruled, treat the answer like any other. If you are instructed that some item of evidence is received for a limited purpose only, you must follow that instruction.
Id. Vol. VII Doc. 190 at 128. At the close of evidence, the judge again instructed the jury on these points:
The Court did not by any words uttered during the trial, and the Court does not by these instructions give or intimate, or wish to be understood by you as giving or intimating, any opinions as to what has or has not been proven in this case, nor as to what are or are not the facts in this case.
...
It is the duty of the attorney on each side of the case to object when the other side offers testimony or other evidence which the attorney believes is not properly admissible. You should not show prejudice against an attorney or his client because the attorney has made objections.

*1169 Upon allowing testimony or other evidence to be introduced over the objection of any attorney, the Court does not, unless expressly stated, indicate any opinion as to the weight or effect of any such evidence. As stated before, the jurors are the sole judges of the credibility of all witnesses and the weight and effect of all evidence.
When the Court has sustained an objection to a question addressed to a witness, the jury must disregard the question entirely, and may draw no inference from the wording of it or speculate as to what the witness might have said if he or she had been permitted to answer the question.
...
Your verdict must be based solely upon the evidence received in the case. Nothing you have seen or read outside of court may be considered. Nothing that I have said or done during the course of this trial is intended in any way to somehow suggest to you what I think your verdict should be. Nothing said in these instructions and nothing in any form of verdict prepared for your convenience is to suggest or convey to you in any way or manner any intimation as to what verdict I think you should return. What the verdict shall be is the exclusive duty and responsibility of the jury. As I have told you many times, you are the sole judges of the facts.
Id. Vol. II Doc. 109 at 11-12, 44, 46-47. In light of these instructionswhich juries are presumed to follow, see United States v. Meridyth, 364 F.3d 1181, 1184 (10th Cir.2004)we hold that the judge's comments in the jury's presence did not deny Defendants a fair trial. See United States v. Harrison, 296 F.3d 994, 1007 (10th Cir. 2002) (rejecting judicial-misconduct claim in part because judge instructed jury that it should not infer from his conduct that he had any opinion on the issues before the jury).
We now turn to Defendants' claim that the trial judge's bias required recusal under 28 U.S.C. § 455. The issue before us is whether "sufficient factual grounds exist to cause a reasonable, objective person, knowing all the relevant facts, to question the judge's impartiality." United States v. Pearson, 203 F.3d 1243, 1277 (10th Cir.2000). The factual grounds relied upon by Defendants all concern the conduct of the trial itself. Such evidence ordinarily will not suffice to establish bias warranting recusal. As the Supreme Court has stated: "[J]udicial rulings alone almost never constitute a valid basis for a bias or partiality motion.... [They] can only in the rarest circumstances evidence the degree of favoritism or antagonism required" for recusal. Liteky v. United States, 510 U.S. 540, 555, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994). And "[a] judge's ordinary efforts at courtroom administrationeven a stern and short-tempered judge's ordinary efforts at courtroom administrationremain immune." Id. at 556, 114 S.Ct. 1147. "[E]xpressions of impatience, dissatisfaction, annoyance, and even anger, that are within the bounds of what imperfect men and women, even after having been confirmed as federal judges, sometimes display" do not support a bias challenge "unless they display a deep-seated favoritism or antagonism that would make fair judgment impossible." Id. at 555-56, 114 S.Ct. 1147. Our examination of the matters raised in Defendants' briefs (including statements by the judge outside the jury's presence) reveals that the district judge's conduct fell far short of the sort of impropriety that would support reversal for failure to recuse under § 455.
The district court did not err in denying Defendants' motion for a new trial on the ground of bias.


*1170 D. Ms. Erickson's Ineffective-assistance Claim
Finally, Ms. Erickson contends that her trial counsel rendered ineffective assistance by failing to use Exhibit 4-B to cross-examine McCurdy. We decline to address the issue. As the Supreme Court has stated, "[I]n most cases a motion brought under [28 U.S.C.] § 2255 is preferable to direct appeal for deciding claims of ineffective assistance." Massaro v. United States, 538 U.S. 500, 504, 123 S.Ct. 1690, 155 L.Ed.2d 714 (2003). Even before Massaro this circuit had held that it is never necessary to bring an ineffectiveness claim on direct appeal because collateral proceedings under 28 U.S.C. § 2255 are almost always preferable. We explained: "A factual record must be developed in and addressed by the district court in the first instance for effective review. Even if evidence is not necessary, at the very least counsel accused of deficient performance can explain their reasoning and actions, and the district court can render its opinion on the merits of the claim." United States v. Galloway, 56 F.3d 1239, 1240 (10th Cir.1995) (en banc) (footnote omitted). We see no reason here to depart from the general rule that ineffective-assistance claims should not be addressed on direct appeal.

III. CONCLUSION
We AFFIRM the district court.
NOTES
[1]  A second letter from another commissioner mentions Ashdown and the audit but says nothing about Ashdown's knowledge of it; nor does it suggest what the audit results were.
[2]  Mr. Mitchell's reply brief on appeal points to two affidavits asserting that Exhibit 4-B was not made available to Defendants before trial. One is by Mr. Mitchell's sister, who kept records at Mitchell Construction. The other was by a paralegal for Ms. Erickson's posttrial and appellate counsel. It is questionable whether the affiants could have had personal knowledge of what was made available to Defendants in the government's open file; but we do not consider their affidavits in any event, because they were not referenced in Mr. Mitchell's opening brief, so the government had no opportunity to challenge them. See Stump v. Gates, 211 F.3d 527, 533 (10th Cir.2000) (court does not ordinarily consider matters raised for first time in reply brief).
