
560 F.3d 566 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Patrick CARSON (05-1812); Robert Hey (05-1889); Peter Jacquemain (05-2143), Defendants-Appellants.
United States of America, Plaintiff-Appellant/Cross-Appellee,
v.
Robert Jacquemain, Defendant-Appellee/Cross-Appellant.
Nos. 05-1812, 05-1889, 05-2143, 05-2294, 05-2295.
United States Court of Appeals, Sixth Circuit.
Argued: May 1, 2008.
Decided and Filed: March 30, 2009.
*570 ARGUED: Steven F. Fishman, Law Office, Detroit, Michigan, Michael C. Naughton, Law Offices, Detroit, Michigan, Spiros P. Cocoves, Law Office, Toledo, Ohio, Scott C. Holbrook, Baker & Hostetler, Cleveland, Ohio, for Defendant. Daniel R. Hurley, Assistant United States Attorney, Detroit, Michigan, for Plaintiff. ON BRIEF: Steven F. Fishman, Law Office, Detroit, Michigan, Spiros P. Cocoves, Law Office, Toledo, Ohio, Scott C. Holbrook, Daniel R. Warren, Baker & Hostetler, Cleveland, Ohio, James C. Thomas, Plunkett & Cooney, Detroit, Michigan, for Defendant. Daniel R. Hurley, Assistant United States Attorney, Detroit, Michigan, Angela M. Miller, Diane K. Flynn, United States Department of Justice, Washington, D.C., for Plaintiff.
Before: GUY, SUHRHEINRICH, and GIBBONS, Circuit Judges.

OPINION
JULIA SMITH GIBBONS, Circuit Judge.
This case arises out of the assault of Robert Paxton by Mount Clemens Police Department officers and the officers' subsequent conspiracy to conceal this assault. Following a joint trial of five defendants, the jury convicted Patrick Carson of deprivation of rights under color of law, conspiracy to obstruct justice, and obstruction of justice. The jury found Robert Hey guilty of obstruction of justice and perjury. Peter Jacquemain was found guilty of obstruction of justice, and Robert Jacquemain was found guilty of conspiracy to obstruct justice. A fifth officer, Daniel Gerkey, was acquitted of all charges.
Carson, Hey, and the Jacquemains appeal their convictions on various grounds, and Carson appeals his sentence. Additionally, the government appeals the sentence of Robert Jacquemain. For the reasons set forth below, we affirm the convictions of Carson, Hey, and the Jacquemains. Additionally, we affirm Carson's sentence. We also conclude that any errors in calculating Robert Jacquemain's sentence were harmless and that his sentence was not substantively unreasonable. We therefore affirm Robert Jacquemain's sentence.

I.
On the evening of July 27, 2002, Robert Hey, an off-duty Mount Clemens police officer, was driving in his vehicle with a friend, Brian Pike. Hey and Pike were on their way to the Mount Clemens police station when Hey noticed that a vehicle was tailgating his own. The driver of the tailgating vehicle, Robert Paxton, believed that Hey had cut him off as he was approaching a traffic light. This encounter lead to escalating road rage, with both parties tailgating, cutting each other off, and braking abruptly.
Hey then placed a call on his cell phone to the Mount Clemens police station and requested assistance, stating that someone *571 was trying to run him off the road. At the time, Mount Clemens police officers Duane Poucher, Patrick Carson, Peter Jacquemain, Robert Jacquemain, and Daniel Gerkey were on duty at the station. The five officers ran to their patrol cars. Poucher and Gerkey left the station first, in one patrol car; Robert Jacquemain then departed with Carson, and Peter Jacquemain drove alone. Poucher and Gerkey reached Hey's vehicle and passed it in pursuit of Paxton's vehicle. Paxton eventually pulled over in a residential neighborhood, on the right side of the street, and Poucher, the driver of the patrol car, parked at an angle behind Paxton's vehicle. Carson and Robert Jacquemain arrived next, parking on the side and slightly in front of Poucher's patrol car. Peter Jacquemain stopped his car behind Poucher's, and Hey parked on the left side of the street.
According to the testimony of Poucher, upon exiting his patrol car, Robert Jacquemain ran to Paxton's vehicle, opened the driver's side door, pulled Paxton out of the vehicle, and threw Paxton on the ground, head first.[1] Other officers also approached Paxton's vehicle. Poucher then exited his patrol car and observed the four other officers crouched around Paxton, holding him down. Then, in view of several neighborhood residentsTracey Anderson, Heather Lane, and Joseph Burkhardtthe officers beat Paxton. Paxton did not resist the officers; instead, he shielded himself and pled with the officers to stop. Poucher testified that Carson struck Paxton at least twice, and Poucher himself admitted that he kicked Paxton two or three times in the groin area. The bystandersPike, Anderson, Lane, and Burkhardttestified, with varying degrees of detail, that they saw the officers punching and kicking Paxton while he was on the ground. The bystanders did not, however, specifically identify any officers who hit Paxton. Additionally, two bystanders reported that the officers were yelling profanities at Paxton, and Anderson testified that the officers told Paxton "that will teach him to go up against a police officer."
Robert Jacquemain, the only officer who testified at trial, painted a different picture of the incident. According to Jacquemain, Paxton exited his vehicle on his own, waved his clenched fists at the officers, and did not obey when Jacquemain told him to get down. When Paxton came toward him, Jacquemain, in fear of his own safety, tackled him to the ground. Jacquemain testified that Paxton resisted arrest and struggled with the officers. Additionally, Jacquemain denied punching or kicking Paxton.
Eventually, the officers handcuffed Paxton and put him in a patrol car.[2] Robert Jacquemain and Carson drove Paxton to the Mount Clemens police station. Hey and Pike exited their vehicle only after Paxton had been handcuffed and taken away from the scene. Anderson, one of the neighborhood residents, testified that the remaining officers and Pike lingered at the scene for a few minutes, talking, smoking, and laughing. The officers then returned to the police station. At the police station, Paxton was handcuffed and booked. Paxton was eventually taken to the hospital for treatment of his injuries. He had a number of abrasions and lacerations *572 on his face; his right eye was bruised, and he received stitches.
When Poucher returned to the station, he found Robert Jacquemain and Hey in the squad room. Poucher testified that Robert Jacquemain told him that "we're going to say that he got out of the car, we're going to say that he came at us." Poucher interpreted this to mean that Paxton had been physically injured, and, thus, the officers were going to report that Paxton was the aggressor to avoid "get[ting] in trouble for beating him up." According to Poucher, the officers had discussions regarding their reports, and he was given a copy of Carson's report as a template, so that the reports would coincide with one another. Each officer's report, with the exception of Hey's, indicated that Paxton was the aggressor. The reports of Carson, Poucher, Peter Jacquemain, and Robert Jacquemain all stated that Paxton exited his vehicle, charged at the officers in a threatening manner, and struggled with the officers. Hey's report only recounted his road rage incident with Paxton and merely noted that he observed Paxton's vehicle parked near the patrol cars.
Raymond Langley, a Mount Clemens detective, prepared a warrant request based on these reports. The warrant request recommended that criminal charges be brought against Paxton for felonious assault with a motor vehicle, resisting arrest, and fleeing and eluding. The county prosecutor authorized the warrant and prepared a formal felony complaint.
On October 3, 2003, a preliminary examination was held at the Macomb County District Court to ascertain whether there was sufficient evidence to proceed with criminal charges against Paxton.[3] The prosecutor called Carson and Robert Jacquemain as witnesses. Both officers testified that Paxton exited his car in an aggressive fashion and resisted arrest.[4]
Paxton subsequently filed a civil lawsuit against the city and the officers. Poucher testified that, when he spoke with Robert Jacquemain about Paxton's lawsuit, Jacquemain said that "we needed to stick to the story about [Paxton] getting out of his vehicle." In response to the civil suit, a supervisor at Mount Clemens Police Department launched an internal investigation of the officers. Poucher testified that he thereafter spoke with Carson and Robert Jacquemain and confirmed that he would "stick to the fabricated story."[5] Additionally, the FBI began to investigate the incident. During an interview with an FBI agent in March 2003, Robert Jacquemain again asserted that Paxton exited his vehicle on his own, waving his fists. Jacquemain told the agent that he did not see any officers strike or kick Paxton.
In August and September 2003, a federal grand jury investigated the incident. When called to testify, Hey stated he saw nothing and heard nothing with respect to Paxton's arrest. Hey testified that he did not see how Paxton was removed from his car; rather, he only saw Paxton in the rear of the patrol car after he had been taken into custody. Hey further stated that he *573 saw no officers on the scene during the arrest, until Peter Jacquemain walked toward his vehicle after Paxton was in custody. Hey recalled that, when he and Pike were sitting in the vehicle, they discussed the fact that there was "fighting" going on at the scene.
On May 26, 2004, a grand jury returned a nine-count second superseding indictment against Carson, Hey, the Jacquemains, and Gerkey. Count I alleged that Carson, the Jacquemains, and Gerkey assaulted Paxton, thereby depriving Paxton of his constitutional rights under color of law, in violation of 18 U.S.C. § 242. Count II charged Carson, the Jacquemains, Gerkey, and Hey with conspiring to cover up the beating of Paxton, in violation of 18 U.S.C. § 371. Counts III through VI alleged that Carson, the Jacquemains, and Gerkey obstructed justice by filing false police reports, in violation of 18 U.S.C. § 1512(b)(3). Count VII charged Hey with obstructing justice by giving false and misleading grand jury testimony, in violation of 18 U.S.C. § 1503.[6] Count VIII charged Hey with perjury, in violation of 18 U.S.C. § 1623, for providing materially false information to a grand jury. Finally, Count IX alleged that Hey obstructed justice, in violation of 18 U.S.C. 1512(c)(2), for providing false and misleading testimony to a grand jury.[7]
On June 9, 2004, the joint trial of Carson, Hey, the Jacquemains, and Gerkey commenced. The jury found Carson guilty on Counts I, II, and III (deprivation of rights, conspiracy, and obstruction of justice). Hey was convicted on Counts VIII and IX (perjury and obstruction of justice). Peter Jacquemain was convicted of Count V (obstruction of justice) and acquitted on Counts I and II (deprivation of rights and conspiracy). Robert Jacquemain was convicted on Count II (conspiracy to obstruct justice) and acquitted on Counts I and IV (deprivation of rights and obstruction of justice). Gerkey was acquitted of all charges.
After the trial concluded, Robert Jacquemain filed a motion for judgment of acquittal, pursuant to Federal Rule of Criminal Procedure 29, which Hey joined. Hey also filed a motion for judgment of acquittal, as well as a motion for a new trial pursuant to Federal Rule of Criminal Procedure 33, which Robert Jacquemain and Carson joined. Peter Jacquemain likewise filed a motion for judgment of acquittal, which Robert Jacquemain and Hey joined. The district court, issuing three orders, denied all of the motions.
The district court sentenced Carson to a term of imprisonment of 33 months. Hey and the Jacquemains were sentenced to three years of probation with six months of home confinement, and Hey was sentenced to an additional six months of community confinement. Each defendant filed a timely notice of appeal. The United States filed a timely notice of appeal of Robert Jacquemain's sentence.

II.
The Jacquemains, Carson, and Hey contend that, during closing argument, the prosecutor committed plain error when he made improper comments regarding the guilty plea of Poucher. Specifically, defendants argue that the prosecutor "repeatedly and deliberately urg[ed] the jury that *574 Poucher's guilty plea to conspiracy was evidence that the conspiracy had in fact taken place." In response, the government argues that the comments were not plainly erroneous, and, even if comments did constitute plain error, they did not affect the defendants' substantial rights.
Whether statements made by a prosecutor amount to misconduct and whether such statements render a trial fundamentally unfair are mixed questions of law and fact, which we review de novo. United States v. Francis, 170 F.3d 546, 549 (6th Cir.1999) (citing United States v. Clark, 982 F.2d 965, 968 (6th Cir.1993)). We employ a two-step test in evaluating a claim of prosecutorial misconduct. See United States v. Gardiner, 463 F.3d 445, 459 (6th Cir.2006). First, we must determine whether the statements were improper. Id. If we conclude the statements were improper, then we must determine whether the remarks were flagrant and thus warrant reversal. Id. We evaluate flagrancy using the following four factors: "(1) whether the conduct and remarks of the prosecutor tended to mislead the jury or prejudice the defendant; (2) whether the conduct or remarks were isolated or extensive; (3) whether the remarks were deliberately or accidentally made; and (4) whether the evidence against the defendant was strong." United States v. Carter, 236 F.3d 777, 783 (6th Cir.2001) (citing United States v. Carroll, 26 F.3d 1380, 1385 (6th Cir.1994)).
Where, as here, a defendant failed to make an objection below, the claim of prosecutorial misconduct is reviewed for plain error. Gardiner, 463 F.3d at 459. "To establish plain error, a defendant must show that: (1) an error occurred in the district court; (2) the error was obvious or clear; (3) the error affected defendant's substantial rights; and (4) this adverse impact seriously affected the fairness, integrity, or public reputation of the judicial proceedings." Id. (quotation marks and citations omitted). We determine whether prosecutorial misconduct affected a defendant's substantial rights by evaluating the four flagrancy factors noted above. Carter, 236 F.3d at 784.
The comments to which the Jacquemains, Carson, and Hey object occurred in succession near the end of the prosecutor's closing argument. The prosecutor stated,
And you'll hear a lot about this deal, this deal that Mr. Poucher got. Well, ask yourselves, as you're hearing about this deal, why is Mr. Poucher, a veteran police officer, going to step up and admit that he committed three felonies if they didn't actually happen? If they didn't happen, what kind of deal is that? What kind of deal is that?
And why is Poucher going to admit to committing three felonies when the best, the best he can receive from the United States government is a recommendation of at least a year in prison? If these felonies didn't happen, why would he take that medicine? Ask yourselves that when you're hearing about Mr. Poucher.
None of the defendants objected to these statements; accordingly, we evaluate them for plain error.

A.
It is well established that the guilty plea of a co-defendant or co-conspirator is never admissible as substantive evidence of a defendant's guilt. United States v. Sanders, 95 F.3d 449, 454 (6th Cir.1996) (citing United States v. Blandford, 33 F.3d 685, 709 (6th Cir.1994)). Such evidence, however, may be considered by the jury in evaluating the co-defendant's credibility as a witness. Id.; United States v. Modena, 302 F.3d 626, 631 (6th Cir.2002). With a *575 limiting instruction, "`evidence of a guilty plea may be elicited by the prosecutor on direct examination so that the jury may assess the credibility of the witnesses the government asks them to believe.'" United States v. Christian, 786 F.2d 203, 214 (6th Cir.1986) (quoting United States v. Halbert, 640 F.2d 1000, 1004 (9th Cir. 1981)). However, "[w]hat may facially appear as a legitimate introduction of evidence of a plea becomes something else and on the level of prejudicial error when, for example, the prosecutor suggests in closing argument that the jury use the plea for a prohibited purpose." Halbert, 640 F.2d at 1005.
As we have previously explained, "[i]n examining prosecutorial misconduct, it is necessary to view the conduct at issue within the context of the trial as a whole." United States v. Beverly, 369 F.3d 516, 543 (6th Cir.2004). When considered in such a manner, the prosecutor's closing argument remarks do not rise to the level of plain error. Throughout the trial, Poucher's guilty plea was mentioned repeatedly by both the prosecution and the defense; the defense sought to question Poucher's credibility by emphasizing that he might obtain a reduced sentence for cooperation with the prosecution, and the prosecution presumably wished to rebut the defense's attempt to impugn Poucher's credibility. See Christian, 786 F.2d at 214.
Poucher's plea was first discussed during opening statements. Clearly anticipating attacks on Poucher's credibility, the prosecutor stated during his opening argument, "You'll probably hear . . . Poucher is a cooperator, he's got a deal with the government so he'll say anything, shouldn't trust him. Fine. We'll prove that these officers were over the line and they knew it through their own actions...." Indeed, in his subsequent opening argument, Carson's attorney recounted the reduced sentence Poucher might obtain for cooperation and told the jurors, "you decide if you want to trust [Poucher's] testimony beyond a reasonable doubt." Later, during direct examination of Poucher, the government introduced evidence of Poucher's guilty plea without objection. The defense attorneys, accordingly, cross-examined Poucher regarding the guilty plea, clearly intending to attack his credibility on this ground.
Thus, when we consider the trial record as a whole, we can infer that the prosecutor's closing argument remarks were intended to address Poucher's credibility, in anticipation of the attacks on his credibility that would follow in the subsequent closing arguments made by the defense. The prosecutor suggested as much just before making the allegedly improper remarks: "And you'll hear a lot about this deal [in the defense's closing arguments], this deal that Mr. Poucher got." Indeed, in the closing arguments that followed, defense counsel repeatedly attacked Poucher's credibility with the evidence of his plea agreement. While the prosecutor's reference to whether the felonies in fact happened was improper, the error was not clear or obvious, given the overall tenor and import of the remarks about Poucher's plea.

B.
Even if the comments did constitute plain error, they must have affected the defendants' substantial rights in order to warrant a new trial. Gardiner, 463 F.3d at 459. We conclude that they did not. To determine whether defendant's substantial rights were affected, we must consider: "(1) whether the conduct and remarks of the prosecutor tended to mislead the jury or prejudice the defendant; (2) whether the conduct or remarks were isolated or extensive; (3) whether the remarks *576 were deliberately or accidentally made; and (4) whether the evidence against the defendant was strong." Carter, 236 F.3d at 783.
As this court has noted, "`[a] guilty plea entered by a co-defendant can be especially prejudicial if the plea is made in connection with a conspiracy to which the remaining defendants are charged.'" Christian, 786 F.2d at 214 (quoting United States v. DeLucca, 630 F.2d 294, 298 (5th Cir.1980)). As noted above, however, Poucher's guilty plea was frequently mentioned throughout the trial for credibility purposes by both the defense and prosecution, because, of course, such a plea can cut both ways in terms of a witness's credibility. See United States v. Townsend, 796 F.2d 158, 163 (6th Cir.1986) ("While the existence of a plea agreement may support the witness' credibility by showing his or her interest in testifying truthfully, the plea agreement may also impeach the witness' credibility by showing his or her interest in testifying as the government wishes regardless of the truth."). Thus, we regard the prosecutors' remarks as referencing Poucher's credibility; the remarks, interpreted in this manner, cannot be said to have misled the jury. Additionally, we note that "the error obviously did not result in a fatal bias against the defendants, since the jury did [fully] acquit one defendant" and acquitted other defendants of some of the charges against them. United States v. Maliszewski, 161 F.3d 992, 1004 (6th Cir.1998); see also United States v. Restaino, 369 F.2d 544, 546 (3d Cir.1966).
In any case, any prejudice resulting from the comments was "cured, or at least minimized, by curative instructions to the jury." Carter, 236 F.3d at 787. "Ordinarily, a court should not overturn a criminal conviction on the basis of a prosecutor's comments alone, especially where the district court has given the jury an instruction that may cure the error." Id. Here, the district court gave a limiting instruction, albeit before the prosecutor's closing argument, with respect to Poucher's plea of guilty, explaining that "[t]he fact that Duane Poucher has pleaded guilty to certain crimes is not evidence that the defendants are guilty, and you cannot consider this against the defendants in any way."
In sum, this factor weighs against finding that the prosecutor's comments affected defendants' substantial rights, as the comments likely did not mislead the jury and the district court admonished the jury not to consider Poucher's guilty plea as evidence of the guilt of his co-defendants.
The prosecutor's remarks were clearly "mere isolated remarks, incapable of infecting the entire trial." Carter, 236 F.3d at 788. The defendants do not allege that any other instances of prosecutorial misconduct took place during this two-week trial. See id. ("If a prosecutor's comments were simply isolated remarks made during the course of a long trial, then the error caused by such misconduct may be harmless."). The prosecutor's three potentially improper comments regarding Poucher's guilty plea were made in rapid succession, comprising no more than half a page of the trial transcript. While "even a single misstep on the part of the prosecutor may be so destructive of the right of the defendant to a fair trial that reversal must follow," see Carter, 236 F.3d at 788 (citations and quotation marks omitted), this is not such a case. Indeed, this case is distinguishable from Carter, in which the court held that the prosecutor committed reversible error when, during closing argument, he misrepresented material evidence and personally attacked opposing counsel. 236 F.3d at 793. In analyzing whether the comments at issue were "isolated or extensive," the court noted that the prosecutor *577 had also acted improperly during voir dire, and, moreover, the comments at issue occurred during the prosecutor's rebuttal argument, making them "the last words from an attorney that were heard by the jury before deliberations." Id. at 788 & n. 7. In contrast to Carter, the comments here were, in fact, isolated and, furthermore, they occurred during the prosecutor's initial closing argument. The defense attorneys had an opportunity to rebut the prosecutor's closing argument by impugning Poucher's credibility in their own, subsequent closing argumentswhich they did. Thus, this factor also weighs against a finding that the prosecutor's comments affected defendants' substantial rights.
The prosecutor repeated his questionable remarks three times, indicating that the comments were made deliberately. More importantly, however, "there is no indication that they stemmed from a deliberate plan to inflame the jury as opposed to unduly-zealous advocacy," United States v. Shalash, 108 Fed.Appx. 269, 281 (6th Cir.2004), particularly given the repeated references to Poucher's guilty plea for credibility purposes throughout all phases of the trial.
The total strength of the evidence against the accused, the final factor we must consider in determining whether the remarks affected defendants' substantive rights, weighs in favor of the government, as the evidence against defendants was sufficiently strong "such that the improper arguments likely had no impact on the outcome of the trial." Modena, 302 F.3d at 635. Certainly, Poucher himself gave extensive testimony that the officers beat Paxton, unprovoked, and then conspired to cover up the beating. Of course, Robert Jacquemain gave conflicting testimony to the contrary. However, Poucher's testimony was further supported by the testimony of four eyewitnessesPike, Anderson, Burkhardt, and Lanewho all indicated that Paxton was beaten during the incident. Moreover, Pike's testimony also indicated that the officers reached into the pickup truck, pulled Paxton out, and took him to the ground head first. Pike's testimony thus supports Poucher's testimony that Paxton was pulled from his vehicle, and it rebuts Robert Jacquemain's testimony that Paxton aggressively exited the vehicle on his own. Thus, Poucher's extensive testimony, when taken in combination with that of the eyewitnesses, indicates that (1) an unprovoked beating took place and (2) the beating was covered up.
In sum, having considered the four flagrancy factors, see Carter, 236 F.3d at 784, we conclude that the prosecutor's remarks did not affect defendants' substantial rights. As explained above, the evidence against defendants was strong; the prosecutor's remarks were isolated and did not stem from a "deliberate plan to inflame the jury"; the prosecutor was likely simply urging the jury to use the plea as evidence of Poucher's credibility; and the district court gave a curative instruction. As such, it is clear that the prosecutor's remarks, even if erroneous, do not warrant a new trial.

C.
Finally, we further note that the prosecutor's remarks, even if erroneous, were not so severe as to "`seriously affect[ ] the fairness, integrity or public reputation of judicial proceedings.'" Carter, 236 F.3d at 783 (quoting United States v. Olano, 507 U.S. 725, 736, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)). Defendants carry the burden of demonstrating that the alleged prosecutorial in the instant case was so "exceptionally flagrant that it constitutes plain error." Modena, 302 F.3d at 635 (quoting Carter, 236 F.3d at 783). Given that the prosecutor's comments were isolated and *578 included among many other references to address Poucher's credibility, the defendants have not met their burden. Accordingly, the prosecutor's comments do not mandate reversal of the convictions of Robert Jacquemain, Peter Jacquemain, Carson, and Hey.

III.
Carson contends that the district court erred when it failed to adopt the exact wording of his proposed jury instruction with respect to one element of Count I (deprivation of rights under color of law, in violation of 18 U.S.C. § 242). Carson requested the following instruction:
In determining whether the force was reasonable, you must consider the fact that police officers are often forced to make split second judgments about the amount of force that is necessary in a particular situation.
As Carson's counsel explained, this language is drawn directly from Graham v. Connor, 490 U.S. 386, 396-97, 109 S.Ct. 1865, 104 L.Ed.2d 443 (1989). The district court declined to use this language, noting that it was "argumentative" and that "neutral standard instructions" were preferable.
As trial courts have broad discretion in drafting jury instructions, we review those instructions only for abuse of discretion. United States v. Jamieson, 427 F.3d 394, 414 (6th Cir.2005). "This Court reviews jury instructions as a whole to determine if they adequately inform the jury of the relevant considerations and provide a basis in law for aiding the jury in reaching its decision and will reverse a jury verdict on account of instructional error only in situations where the instruction, viewed as a whole is confusing, misleading, and prejudicial." United States v. Blackwell, 459 F.3d 739, 764 (6th Cir.2006) (citation, quotation marks, and alterations omitted).
The district court's refusal to deliver Carson's proposed jury instruction requires reversal only "if that instruction is (1) a correct statement of the law, (2) not substantially covered by the charge actually delivered to the jury, and (3) concerns a point so important in the trial that the failure to give it substantially impairs the defendant's defense." United States v. Daniel, 329 F.3d 480, 489 (6th Cir.2003) (quoting United States v. Mack, 159 F.3d 208, 218 (6th Cir.1998)) (internal quotation marks omitted). Carson's claim clearly fails with respect to the second element of this test, as his requested instruction was substantially covered by the instructions actually given to the jury.
The district court gave extensive instructions with respect to the third element of Count I, under which the jury was to determine whether "defendants' conduct... deprived the alleged victim, Robert Paxton, of some right secured or protected by the constitution or laws of the United States; here, the right to be free from the use of unreasonable force by one acting under color of law." The court explained the term "unreasonable force" as follows:
The term unreasonable force means force that has no legitimate law enforcement purpose. A law enforcement officer is justified in using only that amount of force which is reasonably necessary to arrest someone, prevent escape, or defend himself or another from bodily harm. He may not, however, use more force than is reasonably necessary to accomplish these purposes.
In this case, you must determine whether the government has proved beyond a reasonable doubt that the force used against Robert Paxton was unreasonable under all of the circumstances. In other words, you must determine whether a *579 defendant used an amount of force reasonably necessary to arrest Robert Paxton, prevent escape, or defend himself or another against bodily harm, or whether instead the defendant used more force than reasonably necessary to accomplish these purposes.
In determining whether the government has proved beyond a reasonable doubt that the use of force was unreasonable, the defendant's use of force is reviewed from the perspective of a reasonable officer on the scene, rather than with the 20/20 vision of hindsight.
With these instructions, the district court amply conveyed the import of Graham to the jury.
Pursuant to the standard articulated in Graham, "[t]he `reasonableness' of a particular use of force must be judged from the perspective of a reasonable officer on the scene." 490 U.S. at 396, 109 S.Ct. 1865. This inquiry, the Supreme Court explained, is an objective one: "[T]he question is whether the officers' actions are `objectively reasonable' in light of the facts and circumstances confronting them, without regard to their underlying intent or motivation." Id. at 397, 109 S.Ct. 1865. In assessing a claim of unreasonable force pursuant to Graham, this court has explained that "[t]he question we must ask is whether, under the totality of the circumstances, the officer's actions were objectively reasonable." Fox v. DeSoto, 489 F.3d 227, 236-37 (6th Cir.2007). The district court's instructions clearly set out this standard of objective reasonableness for the jury; the court informed the jury that it "must determine whether . . . the force used against Robert Paxton was unreasonable under all of the circumstances" and that "the defendant's use of force is reviewed from the perspective of a reasonable officer on the scene." As the Second Circuit has noted, "Graham requires that the district court impress upon the jury the necessity of assessing whether the force employed by [the officer] was reasonable in light of the particular situation and dangers facing [the officer] at the time." United States v. Schatzle, 901 F.2d 252, 255 (2d Cir.1990). Here, the district court's instructions fulfilled this mandate. Indeed, "[w]e cannot place . . . talismanic weight . . . on Graham's exact wording and do not believe the district court needed to echo the opinion paragraph by paragraph to convey adequately its import to the jury." Id. Accordingly, Carson's argument that the district court abused its discretion in declining to provide the jury with his precise reasonable force instruction is without merit.

IV.
Peter Jacquemain argues that the evidence presented at trial was insufficient to sustain a conviction against him for obstruction of justice, in violation of 18 U.S.C. § 1512(b)(3), as charged in Count V.[8] We review de novo a challenge to the sufficiency of the evidence supporting a criminal conviction. United States v. Kelley, 461 F.3d 817, 825 (6th Cir.2006). In evaluating such a claim, "the court views *580 all evidence in the light most favorable to the prosecution and determines whether there is any evidence from which a reasonable jury could find guilt beyond a reasonable doubt." United States v. Talley, 164 F.3d 989, 996 (6th Cir.1999). To prevail on a sufficiency of the evidence claim, a defendant must demonstrate "that the government failed to prove beyond a reasonable doubt that he committed the elements of the crimes for which he was charged." Id. Thus, the defendant bears a heavy burden when making a sufficiency of the evidence challenge. United States v. Spearman, 186 F.3d 743, 746 (6th Cir.1999).
The statute Jacquemain was charged with violating provides, in relevant part, "[w]hoever knowingly . . . engages in misleading conduct toward another person, with intent to . . . hinder, delay, or prevent the communication to a law enforcement officer or judge of the United States of information relating to the commission or possible commission of a Federal offense" shall be fined, imprisoned, or both. 18 U.S.C. § 1512(b)(3). Thus, in order to obtain a conviction for obstruction of justice under 18 U.S.C. § 1512(b)(3), the government must prove that the defendant (1) knowingly and willfully engaged in misleading conduct toward another person, (2) with the intent to hinder, delay, or prevent the communication of information to a federal official, (3) about the commission or the possible commission of a federal crime. United States v. Ronda, 455 F.3d 1273, 1284 (11th Cir.2006) (citing United States v. Veal, 153 F.3d 1233, 1253 (11th Cir. 1998)).
As in his motion for judgment of acquittal before the district court, Peter Jacquemain concedes on appeal that the evidence was sufficient to establish the first and third elements of the offense. Jacquemain, however, argues that the evidence was insufficient to establish that the misleading conduct was committed with the intent to hinder, delay, or prevent communication of truthful information about the possible federal offense to a federal law enforcement officer.[9] Specifically, Jacquemain contends that, because his misleading report was prepared contemporaneously with the incidentwhich was six months before the federal investigation beganthe government failed to establish the requisite federal nexus to sustain his conviction. This argument is without merit.
Although this circuit has never considered the issue, other courts have examined and rejected similar "lack of federal nexus" arguments. As the Eleventh Circuit has noted on more than one occasion, "§ 1512(b)(3) does not require a specific intent to mislead federal officials." Ronda, 455 F.3d at 1285 (citing Veal, 153 F.3d at 1252). Instead, the court explained, "[f]or violation of § 1512(b)(3), it is sufficient if the misleading information is likely to be transferred to a federal agent." Id. (quoting Veal, 153 F.3d at 1251); see also *581 18 U.S.C. § 1512(g) (stating that, in a § 1512 prosecution, no state of mind need be proved with respect to whether the officials or proceedings that received the misleading information were federal officials or proceedings). Accordingly, in Ronda and Veal, in which the defendants only misled state investigators, there was nonetheless a violation of § 1512(b)(3) because of "the possibility or likelihood that their false and misleading information would be transferred to federal authorities irrespective of the governmental authority represented by the initial investigators." Id. (quoting Veal, 153 F.3d at 1251-52); see also United States v. Baldyga, 233 F.3d 674, 680 (1st Cir.2000) (same). The court explained the rationale underlying this standard: "[F]ederal jurisdiction under § 1512(b)(3) is based on the federal interest of protecting the integrity of potential federal investigations by ensuring that transfers of information to federal law enforcement officers and judges relating to the possible commission of federal offenses be truthful and unimpeded." Ronda, 455 F.3d at 1286-87 (quoting Veal, 153 F.3d at 1250).
Thus, where, as here, the government has established that all police officers in Michigan receive training regarding the consequences of the use of excessive force, a reasonable jury could conclude that Peter Jacquemain knew that writing a misleading report to cover up the use of excessive force might result in a federal investigation. At trial, the government read into evidence a joint stipulation stating that the training given to all officers in Michigan "included instruction that if officers use excessive force they could be prosecuted in state or federal court." The government also introduced into evidence Jacquemain's community college transcript and police academy training records, which indicate that he had received this training. Additionally, Poucher testified that he understood that it is illegal for a police officer to assault a citizen "under color of law," and, moreover, he understood that the intent behind writing the misleading reports was to avoid the repercussions for assaulting Paxton under color of law. As the district court noted, the jury could infer from this testimony and evidence that, at the time Peter Jacquemain penned his false police report, he intended to avoid a possible federal prosecution for using excessive force.
Jacquemain, however, argues that Arthur Andersen LLP v. United States, 544 U.S. 696, 125 S.Ct. 2129, 161 L.Ed.2d 1008 (2005), altered the legal landscape with respect to § 1512 convictions, and, accordingly, mere possibility of a federal investigation is no longer sufficient to satisfy the intent element of a § 1512(b)(3) conviction. In Arthur Andersen, the Supreme Court reversed a corporation's conviction for obstruction of justice in violation of 18 U.S.C. § 1512(b)(2). The corporation had been convicted of violating § 1512(b)(2)(A) and (B) for corruptly persuading its employees to withhold documents from an official proceeding and destroy documents with the intent to impair the documents' availability for use in an official proceeding. Id. at 702, 125 S.Ct. 2129. The Court found that the jury instructions regarding these offenses were infirm because, inter alia, "[t]hey led the jury to believe that it did not have to find any nexus between the `persua[sion]' to destroy documents and any particular proceeding." Id. at 707, 125 S.Ct. 2129. The Court explained, "[a] `knowingly ... corrup[t] persaude[r]' cannot be someone who persuades others to shred documents under a document retention policy when he does not have in contemplation any particular official proceeding in which those documents might be material." Id. at 708, 125 S.Ct. 2129 (emphasis added). Thus, *582 Jacquemain appears to argue, the government in this case was required to show, per Arthur Andersen, a nexus between the misleading report and a particular proceeding.
In rejecting this precise argument, the Eleventh Circuit emphasized the differences between § 1512(b)(2)the statute at issue in Arthur Andersenand § 1512(b)(3). Ronda, 455 F.3d at 1288. The court noted that § 1512(b)(3) does not contain the "an official proceeding" language, as does § 1512(b)(2). Id. Rather, § 1512(b)(2) is less strict in its choice of words, as it "requires only that a defendant intended to hinder, delay, or prevent communication to any `law enforcement officer or judge of the United States.'" Id. We agree with the Eleventh Circuit's analysis; Arthur Andersen does not require the courts to "graft onto § 1512(b)(3) `an official proceeding' requirement based on statutory language in § 1512(b)(2) that does not appear in § 1512(b)(3)." Id.; see also United States v. Byrne, 435 F.3d 16, 24-25 (1st Cir.2006) (concluding that Arthur Andersen was irrelevant to sufficiency of the evidence claim for § 1512(b)(3) conviction).
The government, accordingly, has presented sufficient evidence from which a reasonable jury could find that Peter Jacquemain's intent was to hinder the communication of truthful information to federal law enforcement officers when he provided misleading information to federal law enforcement officers.

V.
Hey challenges the sufficiency of the evidence supporting both his conviction for obstruction of justice pursuant to 18 U.S.C. § 1512(c)(2) and his conviction for perjury under 18 U.S.C. § 1623. Both convictions stem from the false testimony Hey provided on September 18, 2003, before a grand jury. When called to testify, Hey stated he saw nothing and heard nothing with respect to Paxton's arrest.[10] Hey testified that he did not see how Paxton was removed from his car. Rather, Hey claimed he only saw Paxton in the rear of the patrol car after he had been taken into custody. He further stated that he saw no officers on the scene during the arrest, until Peter Jacquemain walked toward his vehicle after Paxton was in custody.[11] Hey recalled that, when he and Pike were sitting in the vehicle, they discussed the fact that there was "fighting" going on at the scene.
The testimony of Brian Pikethe passenger in Hey's vehiclestarkly contrasted with that provided by Hey. At trial, Pike, who was sitting in the passenger seat while Hey sat in the driver's seat, testified that they followed Paxton's vehicle through a residential neighborhood until it came to a stop on the right-hand side of the road. Pike stated that Hey's vehicle stopped on the left side of the road, from where he had an unobstructed view of Paxton's vehicle and the police car to its left. He further noted that the street lights, headlights, and flashing lights on the police cars illuminated the scene. Indeed, *583 Pike saw Paxton's exit from his vehicle: He stated that saw police officers reach into Paxton's vehicle, pull Paxton out of the car head first, and take Paxton to the ground. Pike testified that he saw the officers surround Paxton and observed their "arms going up and down, striking blows like a punching or grabbing motion." This scene, Pike estimated, lasted for about a minute. Duane Poucher and the neighborhood eyewitnesses corroborated Pike's testimony indicating that the officers beat Paxton, unprovoked.
Against this factual backdrop, we consider, in turn, each conviction challenged by Hey.

A.
In order to establish a perjury conviction pursuant to 18 U.S.C. § 1623, the government must prove that the defendant (1) knowingly made, (2) a materially false declaration, (3) under oath, (4) in a proceeding before or ancillary to any court of the United States. United States v. Lee, 359 F.3d 412, 419 (6th Cir.2004). Hey disputes only the second element of the offense; he claims that his testimony before the grand jury was neither false nor material.
Viewing the facts in the light most favorable to the prosecution, it is clear that there is ample evidence from which a rational reasonable jury could conclude that Hey gave false grand jury testimony. Hey repeatedly denied that he saw anyone on the scene until Peter Jacquemain walked toward him, after Paxton had been taken into custody. Hey "saw nothing" and "heard nothing" throughout the incident. Yet, the passenger in Hey's vehicle, Pike, sitting inches away from Hey, saw and heard a significant fracas, which he described in detail at trial. Moreover, the neighborhood residents, viewing the incident from various angles and distances, were also able to describe the scene in detail.
Initially, Hey contends that his perjury conviction cannot stand because the grand jury was investigating the identity of persons who may have committed and caused the commission of the civil rights violation, and Hey aided this investigation by identifying the officers present at the scene, whom Hey saw, he claims, after Paxton was taken into custody. However, that Hey accurately testified as to which officers were present at the scene does not relieve Hey of his obligation to truthfully disclose what happened during the incident. The grand jury was attempting to discern what force had been used, which officers used force, and whether this force was reasonable under the circumstances. Hey, however, claimed he saw and heard nothing until after the incident was over.
Additionally, Hey argues that the record is devoid of any evidence that he was in a position to see the incident. This argument is clearly meritless, as "[s]ubstantial and competent circumstantial evidence by itself may support a verdict." Id. at 418 (citation and quotation marks omitted). Indeed, the jury instructions conveyed this to the jurors, who were told, "[t]he law makes no distinction between the weight that you should give to either [direct or circumstantial evidence], or says that one is any better evidence than the other." As noted above, the government presented sufficient evidence from which a reasonable jury could draw the conclusion that, given that a number of other witnesses, including the passenger in Hey's car, saw the incident, Hey was giving false testimony when he claimed to have seen nothing and heard nothing.
Finally, Hey argues that his statements were not material to the grand jury's investigation, apparently because *584 the statements did not result in the grand jury's termination of its investigation and the grand jury received truthful answers from others who testified. As we have explained, however, "a false declaration satisfies the materiality requirement if a truthful statement might have assisted or influenced the grand jury in its investigation." Id. at 417 (quoting United States v. Swift, 809 F.2d 320, 324 (6th Cir.1987)). Moreover, materiality is "measured at the point in time the statement was uttered." Id. (quoting United States v. Sarihifard, 155 F.3d 301, 307 (4th Cir.1998)). Certainly, if Hey had truthfully testified as to what he saw, it would have corroborated Pike's account of the incident and "assisted... the grand jury in its investigation," see id., at the time the testimony was given. The mere fact that Hey's false statements did not "lead the tribunal astray" is, as this court has stated, irrelevant to the materiality analysis. Id.
Hey has not sustained his heavy burden, as it is clear that a rational jury could conclude that he provided materially false testimony to the grand jury.

B.
Pursuant to 18 U.S.C. § 1512(c)(2), "whoever corruptly ... obstructs, influences, or impedes any official proceeding, or attempts to do so," is subject to criminal liability.[12] Hey first contends that the "nexus requirement" has not been satisfied. Pursuant to this requirement, a "defendant's conduct 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.'" United States v. Reich, 479 F.3d 179, 185 (2d Cir.2007) (quoting United States v. Aguilar, 515 U.S. 593, 599, 115 S.Ct. 2357, 132 L.Ed.2d 520 (1995)) (applying Aguilar's "nexus requirement," which was articulated in the context of § 1503, to § 1512(c)(2)). Assuming arguendo that the "nexus requirement" applies to § 1512, Hey's argument fails. Hey's false statements were made "directly to the grand jury itself," see Aguilar, 515 U.S. at 601, 115 S.Ct. 2357, quite unlike the false statements at issue in Aguilar and Reich. The nexus requirement is obviously satisfied here.
Hey also reiterates his argument that there is no direct evidence that he could observe the incident from his vantage point inside his vehicle. As explained supra, there is ample circumstantial evidence from which a jury could conclude that Hey did, in fact, observe the incident but simply lied to the grand jury about it. Accordingly, Hey's sufficiency of the evidence challenge to his § 1512(c)(2) conviction fails.

VI.
After the trial, Hey filed a motion to set aside his conviction, as well as a request for an evidentiary hearing or a new trial pursuant to Federal Rule of Criminal Procedure 33. Hey's request for an evidentiary hearing was premised on the discovery of a "signed document wherein Mr. Paxton, weeks before the trial and arguably within his civil attorney's help, specifically detailed and itemized his injuries, costs and damages." This documenta restitution request Hey received from the Probation Departmentallegedly would prove that Paxton perjured himself at trial. The district court denied Hey's motion on the following grounds: (1) Hey did not identify *585 the allegedly false testimony provided by Paxton; (2) the new evidence was not uniquely in the government's possession as required by Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963) rather, it was in the possession of the Probation Department; and (3) Hey could not show Brady materiality, as Paxton's credibility was not material to the charges on which the jury found Hey guilty. Hey now appeals this determination. We review the district court's decision for abuse of discretion. United States v. Bass, 460 F.3d 830, 838 (6th Cir.2006).
In order to prevail on a Rule 33 motion for a new trial, a defendant must show the following: "(1) the new evidence was discovered after the trial; (2) the evidence could not have been discovered earlier with due diligence; (3) the evidence is material and not merely cumulative or impeaching; and (4) the evidence would likely produce acquittal." United States v. Seago, 930 F.2d 482, 488 (6th Cir.1991) (citations omitted). As the district court correctly noted, Hey cannot prevail on his claim because the evidence is "merely ... impeaching" and it would not "likely produce [an] acquittal." See id. Paxton was questioned at trial regarding his civil lawsuit, in which he sought five million dollars in damages; Paxton claimed that his lawyers calculated this figure. The restitution statement, presumably, could have been used to impeach Paxton's statement that he had not quantified his damages. Mere impeachment evidence, however, is not sufficient to warrant a new trial. See id. Moreover, Paxton's testimony was not central to Hey's convictions, which were supported by the testimony of Poucher, Pike, and the various neighborhood eyewitnesses. Indeed, Paxton was face down during most of the incident and, accordingly, did not give any testimony that would have aided in Hey's convictions for perjury or obstruction of justice.
Thus, the district court did not abuse its discretion in denying Hey's Rule 33 motion.

VII.
Carson challenges the district court's sentence of 33 months imprisonment. We review a district court's sentencing determination for reasonableness, using a deferential abuse-of-discretion standard. Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 594, 169 L.Ed.2d 445 (2007); see also Rita v. United States, 551 U.S. 338, 127 S.Ct. 2456, 2465, 168 L.Ed.2d 203 (2007). Further, we may apply a rebuttable presumption of reasonableness to sentences within the Guidelines range. Rita, 127 S.Ct. at 2462. Reasonableness review has two components: procedural and substantive. Gall, 128 S.Ct. at 597; United States v. Brown, 501 F.3d 722, 724 (6th Cir.2007).
A sentence is procedurally unreasonable if a district court commits a significant procedural error, "such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the [18 U.S.C.] § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence." Gall, 128 S.Ct. at 597. A sentence is substantively unreasonable, according to this court, if "the district court selected the sentence arbitrarily, based the sentence on impermissible factors, failed to consider pertinent § 3553(a) factors, or gave an unreasonable amount of weight to any pertinent factor." United States v. Smith, 510 F.3d 603, 609 (6th Cir.2007) (citing Brown, 501 F.3d at 724).
The district court determined that Carson's base offense level was 20, resulting in *586 an advisory Guidelines range of 33 to 41 months imprisonment. The court sentenced Carson to the low end of the Guidelines range, 33 months.
In his initial brief to the court, Carson challenges only the substantive reasonableness of his sentence. Specifically, Carson contends that his sentence resulted in an unwarranted sentencing disparity and the district court failed to give appropriate weight to this disparity. See 18 U.S.C. § 3553(a)(6) (stating that the sentencing judge shall consider "the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct"). Carson's tried codefendants, Hey and the Jacquemains, were sentenced to three years of probation with six months of home confinement, and Hey was sentenced to an additional six months of community confinement. Poucher, who pleaded guilty to deprivation of rights under color of law, conspiracy to defraud the United States, and obstruction of justice, was sentenced to two years of probation on each count, running concurrently.
Although it is true that § 3553(a)(6) requires a sentencing judge to consider "the need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct," this court has explained that "this factor concerns national disparities between defendants with similar criminal histories convicted of similar criminal conductnot disparities between codefendants." United States v. Conatser, 514 F.3d 508, 521 (6th Cir.2008) (citing United States v. Simmons, 501 F.3d 620, 623-24 (6th Cir.2007) and United States v. LaSalle, 948 F.2d 215, 218 (6th Cir.1991)). Moreover, a number of factors might result in legitimate co-defendant disparities, including "differences in criminal histories, the offenses of conviction, or one coconspirator's decision to plead guilty and cooperate with the government." Id. at 522 (citing United States v. Dexta, 470 F.3d 612, 616 n. 1 (6th Cir.2006) and United States v. Nelson, 918 F.2d 1268, 1275 (6th Cir.1990)). Indeed, two of those factors are present here. The jury convicted Carson of deprivation of rights under color of law, conspiracy to obstruct justice, and obstruction of justice. Thus, Carson was found guilty of more offenses than any of his co-defendants, and he was the only defendant found guilty of deprivation of rights under color of law. Poucher, like Carson, was also convicted of deprivation of rights under color of law, conspiracy to obstruct justice, and obstruction of justice. However, Poucher pleaded guilty and cooperated with the prosecution. Thus, it is evident that the disparity between the co-defendants' sentences was perfectly reasonable.
To be sure, as Carson notes, during the sentencing hearing, the district court noted that it was more concerned with the conduct that occurred after the assault the cover-upthan with the actual assault itself. Thus, Carson argues, there is an unwarranted disparity in the sentences, as his tried co-defendants were convicted of charges related to the cover-up, not the underlying assault. This is not a tenable argument, particularly when one considers the district court's comments during the Jacquemains' sentencing hearing:
Number Six [of the § 3553(a) factors] is the need to avoid unwarranted sentence disparities among defendants with similar records, and in this case, I have given Defendant Patrick Carson, whom I believe to have been by far the most culpable defendant in this case[,] a significant sentence; Defendant Robert Hey, convicted of several counts of perjury and obstruction of justice received probation with six months of community *587 corrections and six months home confinement, and I see Robert and Peter Jacquemain as slightly less culpable than Robert Hey in this case.
Thus, the district court was well aware of the disparities among the defendants' sentences and found Carson to be "most culpable"a reasonable conclusion, given that he was convicted of more offenses than the other defendants.
In his reply brief, Carson raises an entirely new argument: The district court calculated his sentence incorrectly in applying an enhancement for obstruction of justice pursuant to § 3C1.1. We are therefore precluded from considering it. See United States v. Campbell, 279 F.3d 392, 401 (6th Cir.2002) ("[T]he appellant cannot raise new issues in a reply brief; he can only respond to arguments raised for the first time in appellee's brief." (citation omitted)).
The district court calculated and considered the applicable Guidelines range, considered the relevant factors listed in 18 U.S.C. § 3553(a), and considered Carson's arguments for a sentence below the advisory range, which it rejected. Carson's within-Guidelines range sentence is accorded a presumption of reasonableness, Rita, 127 S.Ct. at 2462, and, accordingly, we affirm the district court's sentence as to Carson.

VIII.
Robert Jacquemain was convicted of conspiracy to obstruct justice, for which the district court sentenced him to three years of probation and six months of home confinement. The government appeals Jacquemain's sentence, contending that it is both substantively and procedurally unreasonable.
Under U.S.S.G. § 2X1.1, the base offense level for conspiracy is set at the base offense level of the substantive offense, "plus any adjustments from such guideline for any intended offense conduct that can be established with reasonable certainty." U.S.S.G. § 2X1.1. Section 2J1.2 provides a base offense level of 12 for obstruction of justice. U.S.S.G. § 2J1.2 (2001). However, § 2J1.2(c) further explains, "[i]f the offense involved obstructing the investigation or prosecution of a criminal offense, apply § 2X3.1 (Accessory After the Fact) in respect to that criminal offense, if the resulting offense level is greater than that determined above." Pursuant to § 2X3.1, the base offense level is set at "6 levels lower than the offense level for the underlying offense."
Applying § 2X3.1, the district court looked to § 2H1.1 and determined that 12 was the proper base offense level. The court enhanced the offense level by 6 because "the offense was committed under color of law." U.S.S.G. § 2H1.1(b). The court next increased the offense level by two, pursuant to § 3C1.1, an obstruction of justice enhancement, "because when the defendant engaged in his misleading activity, he knew that the offense he was assisting in covering up included obstructing the investigation." Thus, according to the district court, Jacquemain's base offense level was 20. The district court then subtracted 6 levels, pursuant to § 2X3.1, resulting in a total offense level of 14 and a Guidelines range of 15 to 21 months.
The government requested an additional two-level enhancement under § 3C1.1 for Jacquemain's false testimony at trial. The court declined to apply this, explaining, "I didn't find his testimony in court to be obstructive in any way. I think he told what he could and did it as best he could and I don't believe an enhancement is appropriate based on his testimony." The district court also refused to apply a restraint *588 of victim enhancement under § 3A1.3.
The court then noted that it thought a three-level § 5K2.20 reduction for aberrant behavior was appropriate, resulting in an offense level of 11; however, the court also stated that, even without this departure, a sentence below the Guidelines range was warranted. The court then discussed the § 3553(a) factors extensively and concluded that a below-Guidelines range sentence was appropriate. The court sentenced Jacquemain to three years of probation, including six months of home confinement, and 100 hours of community service.

A. Procedural Reasonableness

The government contends that the district court erred in (1) refusing to apply the § 3C1.1 perjury enhancement, (2) declining to apply a § 3A1.3 restraint of victim enhancement, and (3) granting a downward departure under § 5K2.20.

1. Section 3A1.3 enhancement
Pursuant to § 3A1.3, "[i]f a victim was physically restrained in the course of the offense," the district court must increase the offense level by two. The district court declined to apply this enhancement to Robert Jacquemain's Guidelines calculation, just as it did in Carson's earlier sentencing hearing. The court explained its reasons for denying the enhancement in Carson's sentencing hearing: "[I]t seems to me to be ... kind of piling on to find he was visibly restrained. In addition, there was an ongoing arrest, some restraint was appropriate." The court found that this enhancement would be "duplicative of the underlying offense" for which Carson was already being charged. This court reviews the district court's interpretation of the Guidelines de novo, and its factual findings for clear error. United States v. Tatum, 518 F.3d 369, 372 (6th Cir.2008).
The district court's conclusion that a § 3A1.3 enhancement would be inappropriate because it would be "piling on" and because there was an ongoing lawful arrest implicates both legal and factual issues. In United States v. Clayton, 172 F.3d 347 (5th Cir.1999), the Fifth Circuit examined a similar situation, wherein "[t]he district court concluded that because [the victim] had been lawfully restrained (handcuffed) during the course of a legitimate arresta restraint that was separate from and not done to facilitate the commission of the offense itselfthe two-level victim restraint adjustment, U.S.S.G. § 3A1.3, was not applicable." Id. at 352. In Clayton, a lawfully arrested suspect lay face down and handcuffed on the ground when a police officer kicked the suspect in the head. Id. at 351 n. 4. The Fifth Circuit held that "the lawfulness of the defendant's restraint of the victim at the time the unreasonable or excessive force occurs is not a concern implicated by U.S. S.G. § 3A1.3," and concluded that the district court had erred in failing to apply the enhancement. Id. at 353. We believe that Clayton sets out the appropriate interpretation of § 3A1.3. To the extent that the district court thought that the lawfulness of the arrest precluded application of § 3A1.3, it committed legal error.
Whether the § 3A1.3 enhancement should apply in this case is less clear. The district court's factual findings are cursory. While typically remand for additional factual findings would be appropriate, we conclude that remand is unnecessary here.
In response to the government's § 3A1.3 argument, Jacquemain argues that any error was harmless because the district court also erred in applying the § 3C1.1 enhancement for obstruction of justice, and the errors thus cancel each other out. *589 The court applied "two additional levels under 3C1.1 because when the defendant engaged in his misleading conduct, he knew that the offense he was assisting in covering up included obstructing the investigation." This was, however, incorrect. Pursuant to the § 3C1.1 application note 7:
If the defendant is convicted of an offense covered by ... § 2J1.2 (Obstruction of Justice), [or] ... § 2X3.1 (Accessory After the Fact), ... this adjustment is not to be applied to the offense level for that offense except if a significant further obstruction occurred during the investigation, prosecution, or sentencing of the obstruction offense itself (e.g., if the defendant threatened a witness during the course of the prosecution for the obstruction offense).
§ 3C1.1, cmt. n. 7. The district court made no finding suggesting that "significant further obstruction occurred during the investigation." Thus, Jacquemain's offense is subject to this exception, and, accordingly, the district court erred in applying this enhancement. Looking at the arguments about § 3A1.3 and § 3C1.1 together, it appears that on remand the best outcome for the government, the only appealing party on the sentencing issue, would place this case in its present posturewith a total offense level of 14. Remand would thus serve no purpose.

2. Section 3C1.1 enhancement
The government also contends the district court erred in not applying an additional obstruction of justice enhancement, pursuant to § 3C1.1, for Robert Jacquemain's false testimony at trial. In reviewing § 3C1.1 enhancements, we review the district court's factual findings for clear error and the court's determination of whether the facts constitute an obstruction of justice de novo. United States v. Mise, 240 F.3d 527, 530-31 (6th Cir.2001). Further, we give deference to the district court's credibility findings. Id.
We conclude that the district court did not clearly err in declining to apply this enhancement. The district court stated, "I didn't find his testimony in court to be obstructive in any way. I think he told what he could and did it as best he could and I don't believe an enhancement is appropriate based on his testimony."

3. Section 5K2.20 downward departure
Finally, the government contests the district court's decision to grant a downward departure under U.S.S.G. § 5K2.20. Pursuant to § 5K2.20, "A sentence below the applicable guideline range may be warranted in an extraordinary case if the defendant's criminal conduct constituted aberrant behavior." U.S.S.G. § 5K2.20 (2001). Application note 1 further explains, "`Aberrant behavior' means a single criminal occurrence or single criminal transaction that (A) was committed without significant planning; (B) was of limited duration; and (C) represents a marked deviation by the defendant from an otherwise law-abiding life." U.S.S.G. § 5K2.20 cmt. n. 1 (2001). Here, although this offense may have been a marked deviation from Jacquemain's otherwise law-abiding life, it was not a single criminal transaction that was committed without significant planning. The conspiracy in which Jacquemain took part spanned almost two years and required some level of planning. Thus, the departure was likely not warranted. See United States v. Lepird, 142 Fed.Appx. 880, 881 n. 1 (6th Cir.2005) (affirming refusal to grant § 5K2.20 departure because bank fraud consisted of multiple acts, including depositing counterfeit check and making multiple withdrawals, *590 over a forty-five day period); see also United States v. Hillyer, 457 F.3d 347, 352 (4th Cir.2006) (concluding § 5K2.20 departure should not have been granted where offense involved significant planning and persisted for ten days); United States v. Bueno, 443 F.3d 1017, 1023 (8th Cir.2006) ("The offense must have been more than something out of the defendant's character; it must have been a spontaneous and thoughtless act.").
The district court, however, made a finding in the alternative: "I believe [a § 5K2.20 departure] in and of itself would warrant a three-level reduction, which would take this down from a level 14 to a level 11.... However, I still think that when I consider the factors under 3553(a) that a sentence below the guidelines level is warranted." Accordingly, we conclude that the application of § 5K2.20 was harmless error. United States v. Ward, 506 F.3d 468, 477 (6th Cir.2007) ("Sentencing Guidelines range errors that do not affect a defendant's sentence are harmless and do not require a remand for re-sentencing.").

B. Substantive Reasonableness

Finally, we cannot conclude that Jacquemain's sentence is substantively unreasonable. In Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007), the Court explained that while an outside-Guidelines sentence is not afforded a presumption of reasonableness, it is also not presumed to be unreasonable. Id. at 597. An appellate court "may consider the extent of the deviation" from the Guidelines range "but must give due deference to the district court's decision that the § 3553(a) factors, on a whole, justify the extent of the variance." Id. The Court cautioned, "The fact that the appellate court might reasonably have concluded that a different sentence was appropriate is insufficient to justify reversal of the district court." Id. Furthermore, the Court rejected (1) "an appellate rule that requires `extraordinary' circumstances to justify a sentence outside the Guidelines range" and (2) "use of a rigid mathematical formula that uses the percentage of a departure as the standard for determining the strength of the justifications required for a specific sentence." Id. at 594-95. See also United States v. Grossman, 513 F.3d 592, 596 (6th Cir.2008) ("Measured by Gall's requirements and above all by Gall's deference to district court judges at sentencing, the district court did not commit reversible error in reducing Grossman's sentence from 120 months to 66 months.").
In sentencing Jacquemain, the district court exhaustively examined the § 3553(a) factors and amply justified its outside-Guidelines sentence. With respect to the nature and circumstance of the offense, the court noted that the underlying offense "clearly was something that happened quickly, spontaneously, and without the exercise of appropriate judgment." Likewise, the court felt that the responsethe cover-upwas also immediate, impetuous, and without considered judgment, even "if not as spontaneous as the road rage incident." The court found that the history and characteristics of the defendant weighed in favor of a lower sentence. The court noted that it sees a "ton of police misconduct cases," and many police officers that had come before the court had long records of citizen complaints. In contrast, the court explained, Robert Jacquemain had an "unblemished and exemplary record, a lifetime of service in the armed service, many times decorated, and not a single complaint with respect to the citizens [he was] sworn to protect." The court acknowledged that the offense was serious but felt that it was balanced by the "impetuous" nature of the obstruction of *591 justice, "a single line in a police report." The court stated that its sentence would promote respect for the law, and the court thought that there was not any chance the defendant would commit further crimes. The court noted that it felt that Robert Jacquemain was less culpable than Hey and Carson.
Ultimately, the sentence Robert Jacquemain receivedthree years of probation with six months of home confinementis not insignificant. As the Gall Court explained, "[o]ffenders on probation are ... subject to several standard conditions that substantially restrict their liberty." Gall, 128 S.Ct. at 595. Reviewing this sentence under the deferential abuse-of-discretion standard, as we must, id. at 591, we conclude that it is not substantively unreasonable.

IX.
For the reasons set forth above, we affirm the judgment of the district court with respect to each defendant's conviction. We also affirm the sentences of Carson and Robert Jacquemain.
NOTES
[1]  Pike's testimony also indicated that the officers reached into the pickup truck, pulled Paxton out, and took him to the ground head first.
[2]  Another neighborhood resident, John Jones, testified that he saw the officers putting Paxton into a patrol car. Jones stated that the officers rammed Paxton's head into the top of the car, backed him up, and then threw him into the back seat.
[3]  The charges were ultimately dropped by the prosecutor in April 2003.
[4]  Only the transcript of Jacquemain's preliminary examination testimony is included in the joint appendix. However, the testimony of the prosecutor who conducted the examination suggests that both officers testified that Paxton exited his car on his own.
[5]  In sharp contrast to Poucher's testimony, Robert Jacquemain denied conspiring with the other officers to cover up anything about the incident. Jacquemain stated that he never proffered false or misleading information in his reports or to any law enforcement officers, and he asserted that he was innocent of the charges brought against him.
[6]  The government moved to dismiss Count VII before the end of the trial.
[7]  Prior to the second superseding indictment, Duane Poucher pleaded guilty to deprivation of rights under color of law, conspiracy, and obstruction of justice. On September 9, 2005, Poucher was sentenced to two years of probation on each count, running concurrently.
[8]  Count V alleged that "[o]n or about July 27, 2002, . . . [Peter Jacquemain] completed and submitted to officials of the Mount Clemens Police Department a written report containing false and misleading information about the July 27, 2002 traffic stop of Robert Paxton and thereby did knowingly engage in misleading conduct toward another person, with intent to hinder, delay, and prevent the communication to a federal law enforcement officer and federal judge any of the information relating to the commission and possible commission of a federal criminal civil rights offense, under 18 U.S.C. § 242, involving the willful deprivation of Robert Paxton's right to be free from the unreasonable use of force by one acting under color of law."
[9]  Within his sufficiency of the evidence argument, Jacquemain also appears to contend that the jury instructions were improper with respect to the second element of § 1512(b)(3). The district court gave the following instruction regarding the second element, to which Jacquemain did not object:

What the government must prove is that a defendant intended to foreclose the possibility, either temporarily or permanently, that truthful information might be transferred to law enforcement officers who investigate[ ] federal crimes, or courts where such crimes are prosecuted.
However, Jacquemain is apparently objecting to the jury instruction merely because it does not incorporate his novel theory on the element of intent, discussed below, which he draws from Arthur Andersen LLP v. United States, 544 U.S. 696, 125 S.Ct. 2129, 161 L.Ed.2d 1008 (2005). Because this theory is meritless, see infra, this jury instruction was not erroneous.
[10]  The grand jury foreperson captured the essence of Hey's testimony when he asked, "Just try and summarize. You were out on the night in question. You were there. You saw nothing. You heard nothing; is that accurate?" Hey answered, "Well, I sawI saw what happened to me ... But as far as the accusations against the officers, no, I did not see that."
[11]  The prosecutor pressed Hey repeatedly on this point, asking "Is it fair to say from the moment that you arrived on the scene until the moment that Officer Peter Jacquemain walked back to your car, you did not see any person on the scene? ... You didn't see any person[?]" Hey answered, "No, I did not."
[12]  Hey cites to the wrong statute, § 1503, in his brief. Hey was convicted of obstructing justice in violation of § 1512(c)(2).
