#### UNITED STATES of America, Plaintiff-Appellee Cross-Appellant, v. Alexander McQUEEN, Steven Dawkins, Defendants-Appellants Cross Appellees.

No. 12-10840.

United States Court of Appeals, Eleventh Circuit.

Aug. 22, 2013.

*1146Angela Macdonald Miller, Henry C. Leventis, Jessica Dunsay Silver, U.S. Department of Justice, Washington, DC, Wifredo A. Ferrer, Susan R. Osborne, Anne Ruth Schultz, U.S. Attorney’s Office, Miami, FL, for Plaintiff-Appellee-Cross Appellant.

Ari H. Gerstin, Richard A. Sharpstein, Akerman Senterfitt, LLP, Janice Burton *1147Sharpstein, Jorden Burt, LLP, Miami, FL, for Defendant-Appellant-Cross Appellee.

Before BARKETT and MARCUS, Circuit Judges, and CONWAY,* District Judge.

*

 Honorable Anne C. Conway, Chief Judge, United States District Court for the Middle District of Florida, sitting by designation.

MARCUS, Circuit Judge:

Alexander McQueen, a Sergeant at the South Florida Reception Center (“SFRC”), appeals his conviction for conspiring to deprive several inmates of their right to be free from cruel and unusual punishment following a jury trial, in violation of 18 U.S.C. § 241, and for obstruction of justice, in violation of 18 U.S.C. § 1519. Steven Dawkins, a corrections officer at the SFRC, also appeals his conviction for obstruction of justice. Both officers argue that the evidence was insufficient to support their obstruction convictions, the district court gave erroneous jury instructions, and the government improperly bolstered a witness’s testimony. McQueen also claims the evidence was insufficient to sustain the conspiracy charge.

In a cross-appeal, the government contests McQueen’s sentence of a twelve month prison term and Dawkins’s sentence of only one month in jail, arguing that the sentences varied sharply from the recommended Guidelines range — indeed, they varied downward by more than 90% from the bottom of the sentencing range — and were substantively unreasonable. After thorough review, we affirm the convictions but vacate the sentences and remand for resentencing.

I.

A.

The essential facts adduced at trial are these: Scott Butler, Guruba Griffin, Alexander McQueen, and Steven Dawkins (collectively, “the Corrections Officers”) worked as law enforcement officers at the South Florida Reception Center, a state prison in Doral, Florida. A federal grand jury sitting in the Southern District of Florida charged that, on or about February 25, 2009, Butler, Griffin, and McQueen assaulted prisoners, sometimes using broomsticks, as Dawkins idly watched. Count One of the indictment specifically alleged that the four prison guards conspired in violation of 18 U.S.C. § 241 “to injure, oppress, threaten, and intimidate inmates” so as to violate the prisoners’ right “to be free from cruel and unusual punishment.” Count Two charged McQueen with having filed a false report to obstruct justice, in violation of 18 U.S.C. § 1519, and Count Three charged Dawkins with likewise obstructing justice in violation of § 1519.

Although the Corrections Officers were to be tried together, the government sought to introduce Rule 404(b) evidence that Butler and Griffin organized fights among inmates, that they regularly carried broomsticks as weapons, and that Griffin routinely disciplined inmates using extreme and violent measures. Since some of this evidence was relevant *only*as to Griffin and Butler but could unfairly prejudice Dawkins and McQueen, the district court concluded that the trial should engage the services of two petit juries. One jury would hear all the evidence, including evidence of other crimes, wrongs, or acts, *1148and decide Griffin’s and Butler’s fate; the other jury would decide McQueen’s and Dawkins’s cases but would not observe the 404(b) evidence.

Both juries heard an extensive and violent story concerning the abuse and beatings of several inmates at the South Florida Reception Center. Juedline Bertrand and Marvin Woods were housed in the “youthful offender” wing of the prison, where every prisoner under the age of twenty-one and convicted of a felony was kept, segregated and safeguarded from the older inmates in the prison. On February 25, 2009, Bertrand accused Woods of stealing his “honey bun”; a fight broke out between them in an empty room on the second floor of their prison wing. During the fight, Woods smashed his head against an object — a toilet or possibly the metal frame of a bunk bed — causing him to gash his face and bleed. As the fight wound down, the public address system instructed the prisoners to return to their cells. Bertrand returned, but Woods, who was dazed and confused, didn’t move. Officer Griffin, who was going from cell to cell counting the inmates, found Woods in an empty room. When Woods would not disclose who injured him, Griffin ordered every inmate in the wing — two dozen or so — into the day room, demanded that the prisoners get their stories straight, and walked out.

Griffin later returned to the day room with Sergeant McQueen and Officer Dawkins in tow. Griffin asked the assembled inmates who had fought with Woods. No one responded. McQueen was the ranking officer at the time. In retaliation for the prisoners’ silence, McQueen grabbed a broomstick, snapped it in half, and whacked Woods’s legs with the broken broomstick. Woods begged McQueen to stop, but that apparently further enraged the officer, causing him to slam Woods’s head, aggravating Woods’s injury. Officer Griffin, also armed with a broomstick, then turned his attention to inmate Rondell Lyles. Griffin asked Lyles whether he had seen the fight. Lyles said that he had not. Apparently not believing Lyles, Griffin directed Lyles to put his hands on a bench, whereupon he smacked Lyles’s knuckles some three to six times with the broomstick half.

Griffin then asked the assembled inmates if any of them wanted to fight. One prisoner, Branden Pressley, responded that he would brawl with Bertrand. Griffin sanctioned the fight, but imposed certain rules — the fighters were required to box, not wrestle, for three rounds of three minutes each. Not being professional boxers, Pressley and Bertrand violated the rules and, at times, wrestled. When that happened, Griffin and McQueen hit or slapped the violator. At one point, Sergeant McQueen fiercely choked Pressley, who begged McQueen and Griffin to stop the fight. The officers wouldn’t let him quit, however, forcing the fight to continue. When the fight finally ended, Bertrand sucker punched Pressley, which led McQueen to attack Bertrand, again with the broomstick. Tired and overpowered by a corrections officer wielding a broomstick, Bertrand curled into a defensive ball. Griffin came over to Bertrand, reassured him that he could get off the floor, and promised that no one would hurt him any more. But as soon as Bertrand stood up, Griffin slapped or punched his nose, causing it to bleed. Griffin grabbed Bertrand’s throat, choking him with two hands and digging his nails into the inmate’s neck. Griffin converted the choke into a chokehold and held it long enough to knock Bertrand unconscious.

The wanton violence continued on February 25th. Griffin and McQueen proceeded to beat another inmate, Kenneth Stew*1149ard, with the broomstick halves. They did so because Steward had earlier harassed one of Sergeant McQueen’s friends in the medical room. McQueen and Griffin — for no apparent reason — also struck another inmate, Lazaro Martinez, with broomstick halves, striking Martinez’s chest and arms six to eight times. The beatings continued as Griffin and McQueen also pummeled inmate Christopher Jarret with broomsticks. Although somewhere between twenty and twenty-five prisoners witnessed the beatings, only one complained to the prison officials; the others refused to speak in fear of reprisal.

Several prison officials testified at trial. They recounted in some detail the injuries sustained by inmates Bertrand, Jarret, Martinez, Steward, and Woods to their chests, arms, and biceps. The injuries were visible days after the attacks. The officials also testified that corrections officers were required to report *any*violence involving the prisoners, including the use of force by other corrections officers. Nevertheless, two reports — one written by McQueen and the other by Dawkins— downplayed or ignored the repeated acts of violence that occurred on February 25, 2009. Dawkins signed a housing unit log that made no mention of violence or of any fighting. McQueen, who eventually accompanied Woods to the medical station, drafted an incident report about Woods’s injuries. The report falsely failed to recite that Woods was attacked by Sergeant McQueen; rather, it explained that Woods had injured himself while cleaning the shower.

The second of the two petit juries also heard additional testimony concerning Officers Griffin and Butler. Griffin repeatedly warned the prisoners that, if any of them had a problem with another inmate, he would let the two fight. Griffin also forced the arms of at least two prisoners inside ice water filled coolers, waited for the ice water to numb their arms, and then struck their hands with handcuffs or broomsticks.

In the end, the jury found Sergeant McQueen guilty both of conspiring to violate the prisoners’ civil rights and of filing a false report in order to obstruct justice. The same jury, however, found Officer Dawkins not guilty of conspiring to violate the prisoners’ right to be free from cruel and unusual punishment, but concluded that he too was guilty of obstructing justice. The second jury found Butler not guilty, but it could not return a verdict against Officer Griffin, resulting in a mistrial.

B.

The district court scheduled Griffin’s case for a second trial, but instead Griffin entered into a plea agreement whereby he would plead guilty to a *misdemeanor*for willfully depriving one inmate of a right secured by the Constitution in violation of § 242, and thereby face a maximum exposure of only one year in jail. In sharp contrast, both McQueen and Dawkins faced substantially greater prison exposure. Dawkins’s obstruction of justice charge carried a maximum sentence of twenty years’ imprisonment. 18 U.S.C. § 1519. The presentence investigation report (“PSI”) for Dawkins recommended a base offense level of 14 under § 2J1.2(a) of the United States Sentencing Guidelines.1*1150Dawkins had no criminal history, so he had a criminal history category of I, yielding a recommended sentence between fifteen and twenty-one months’ imprisonment.

As for McQueen, his obstruction of justice charge carried a maximum sentence of twenty years in jail, while his conspiracy to violate the inmates’ civil rights charge carried a maximum sentence of ten years’ imprisonment. His base offense level was calculated at 14, U.S.S.G. §§ 2A2.2(a), 2H1.1(a)(1), but the PSI recommended an upward adjustment of 4 levels because McQueen used a dangerous weapon (the broken broomstick) in his assault of the prisoners, *id.*§ 2A2.2(b)(2)(B); of another 3 levels because the inmate victims “sustained bodily injury,” *id.*§ 2A2.2(b)(3)(A); of still another 6 levels because the Sergeant acted “under color of law,” *id.*§ 2Hl.l(b)(l); and finally of 2 more levels because McQueen “willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice with respect to the investigation,” *id.*§ 3C1.1. What’s more, because McQueen assaulted more than five prison inmates, the PSI recommended increasing his offense level by another 5 points, *id.*§ 3D1.4, yielding a total offense level of 34 and a criminal history category of I. The Sentencing Guidelines thus yielded a sentencing range between one-hundred-and-fifty-one and one-hundred-and-eighty-eight months’ imprisonment.

Before sentencing, the district court informed the parties that it was troubled by the disparity between the prison exposure McQueen and Dawkins faced on the one hand and the maximum exposure Griffin faced for a misdemeanor conviction on the other. The court observed that Griffin faced a maximum of only one year of imprisonment and concluded that it could not, in good conscience, sentence McQueen and Dawkins to far heavier prison terms as the Guidelines had suggested. Ultimately, the trial court sentenced McQueen to twelve months’ imprisonment on the § 1519 count and for the § 241 civil rights conspiracy as well, each count to run concurrently with the other — a sentence one-hundred-and-thirty-nine months lower than the bottom of the suggested Guidelines range. The court also placed Sergeant McQueen on supervised release for a term of one year following release from imprisonment. The district court then sentenced Dawkins to a term of only one month’s imprisonment, adding one year of supervised release to Dawkins’s sentence. The district court also imposed a special assessment fee of $200 on McQueen and $100 on Dawkins, but it did not impose any fines. Finally, the district court sentenced Griffin to one year in prison.

Dawkins and McQueen timely appeal their convictions, raising a battery of claimed errors. The government, in turn, has cross-appealed from the sentences, claiming they are substantively unreasonable.

II.

McQueen and Dawkins cite several errors on appeal. First, they both allege the government introduced no evidence that the defendants *knew*they were obstructing a federal investigation, which they claim was required by 18 U.S.C. § 1519. McQueen also separately argues that the evidence was insufficient to establish beyond a reasonable doubt either that he joined an unlawful conspiracy to violate the inmates’ civil rights, or that he obstructed justice. Both defendants also claim that the trial court’s jury instructions were erroneous, and that the government improp*1151erly bolstered the testimony of a witness.2

A.

McQueen and Dawkins first claim that the district court misread the obstruction of justice statute, arguing that § 1519 requires the government to prove that the defendants falsified a document with the intent to impede or obstruct an actual or contemplated *federal*investigation. And since there was no evidence that McQueen and Dawkins knew of any ongoing or contemplated federal investigation, the argument continues, there was- insufficient evidence to convict either Dawkins or McQueen. We are unpersuaded.

We review the interpretation of a statute *de novo. United States v. Johnson,*399 F.3d 1297, 1298 (11th Cir.2005). We begin as always with the text of the statute. *Harris v. Garner,*216 F.3d 970, 972 (11th Cir.2000) (en banc). Section 1519 reads this way:

> Whoever knowingly alters, destroys, mutilates, conceals, covers up, falsifies, or makes a false entry in any record, document, or tangible object with the intent to impede, obstruct, or influence the investigation or proper administration of any matter within the jurisdiction of any department or agency of the United States or any case filed under title 11, or in relation to or contemplation of any such matter or case, shall be fined under this title, imprisoned not more than 20 years, or both.

18 U.S.C. § 1519. Section 1519’s language requires only that a criminal defendant “knowingly” alter, destroy, mutilate, conceal, cover up, falsify, or make a false *1152entry. There is nothing in the language that says the defendant must also know that any possible investigation is federal in nature. In fact, McQueen and Dawkins’s “federal investigation” requirement may be inferred only from the following language: “any matter within the jurisdiction of any department or agency of the United States.” But, as we see it, “any matter within the jurisdiction” is merely a jurisdictional element, for which no mens rea is required. *See United States v. Campa,*529 F.3d 980, 1006 (11th Cir.2008) (“[N]o proof of mens rea is necessary for elements that are ‘jurisdictional only.’ ”); *accord United States v. McRae,*702 F.3d 806, 835 (5th Cir.2012) (“[TJhe mens rea of a federal criminal statute does not ordinarily extend to the statute’s jurisdictional elements.”); cf. *United States v. Yermian,*468 U.S. 63, 68, 104 S.Ct. 2936, 82 L.Ed.2d 53 (1984) (finding “any matter within the jurisdiction of any department or agency of the United States” to be a jurisdictional requirement). In short, we do not see how “knowingly” can be said to fairly modify the language “within the jurisdiction of ... the United States.”

Every court of appeals that has addressed this issue has reached the same conclusion. Thus, for example, the Third Circuit in' *United States v. Moyer*rejected the same argument made by Dawkins and McQueen, because the “most natural reading of § 1519 ... is to interpret ‘knowingly’ as modifying its surrounding verbs only: ‘alters, destroys, mutilates, conceals, covers up, falsifies, or makes a false entry.’ ” 674 F.3d 192, 208 (3d Cir.2012). As the Third Circuit saw it, “any matter within the jurisdiction” was plainly a jurisdictional element, and “[i]t is well settled that mens rea requirements typically do not extend to the jurisdictional elements of a crime.” *Id.*Similarly, in *United States v. Yielding,*the Eighth Circuit sustained the following jury instruction in a § 1519 case: “In order to meet its burden, the United States need not prove that the defendant specifically knew that the matter was within the jurisdiction of a department or agency.” 657 F.3d 688, 710 (8th Cir.2011). The Eighth Circuit concluded that the instruction accurately stated the law because the “most natural grammatical reading ... is that the term ‘knowingly’ in § 1519 modifies only the surrounding verbs.” *Id.*at 714. Therefore, “[i]t is sufficient that the ‘matter’ [under investigation] is within the jurisdiction of a federal agency as a factual matter,” *Id.*(citation omitted); *see also United States v. Gray,*642 F.3d 371, 378 (2d Cir.2011) (“By the plain terms of § 1519, knowledge of a pending federal investigation or proceeding is not an element of the obstruction crime.”); *United States v. Kernell,*667 F.3d 746, 752-56 (6th Cir.) (same), *cert. denied,*— U.S. -, 133 S.Ct. 259, 184 L.Ed.2d 45 (2012).

This conclusion is amply supported by § 1519’s legislative history. The Senate Report observed that “[t]his statute is specifically meant *not*to include any technical requirement, which some courts have read into other obstruction of justice statutes, *to tie the obstructive conduct to a pending or imminent proceeding or matter.”*S.Rep. No. 107-146, at 14-15 (2002) (emphases added); *see also United States v. Fontenot,*611 F.3d 734, 739 (11th Cir.2010) (Barkett, J., specially concurring) (noting that legislative history showed § 1519 was not meant to be read narrowly, as the obstruction statute in *Aguilar*was). According to Senator Leahy, who was a principal author of the legislation, “[t]he fact that a matter is within the jurisdiction of a federal agency is intended to be a jurisdictional matter, and not in any way linked to the intent of the defendant.” 148 Cong. Rec. S7419 (daily ed. July 26, 2002) (statement- of Sen. Patrick Leahy). “Rather, the intent required is the intent to obstruct, *1153not some level of knowledge about the agency processes [or] the precise nature of the agency [or] court’s jurisdiction.” *Id.*In short, the defendants’ interpretation finds little support in the text of the statute, in its legislative history, or in the case law, and we reject it.

B.

McQueen also raises a sufficiency argument about the conspiracy conviction, claiming there was no evidence of any plan or agreement to interfere with the civil rights of the inmates and no evidence that he knowingly joined any conspiracy. “We review the sufficiency of the evidence *de novo,*viewing the evidence in the light most favorable to the verdict.” *United States v. Tobin,*676 F.3d 1264, 1289 (11th Cir.2012) (quoting *United States v. Chirino-Alvarez,*615 F.3d 1344, 1346 (11th Cir.2010) (per curiam)).

The statute — 18 U.S.C. § 241— makes it a crime for “two or more persons [to] conspire to injure, oppress, threaten, or intimidate any person in any State ... in the free exercise of enjoyment of any right or privilege secured to him by the Constitution or laws of the United States.” “Conspiracy is the gravamen of the offense under 18 U.S.C. § 241.” *United States v. Purvis,*580 F.2d 853, 859 (5th Cir.1978).3 “To sustain a conviction for conspiracy, the government must prove (1) ‘the existence of an agreement to achieve an unlawful objective’; (2) ‘the defendants’] knowing and voluntary participation in the conspiracy’; and (3) ‘an overt act in furtherance of the conspiracy.’ ” *United States v. Ibarguen-Mosquera,*634 F.3d 1370, 1385 (11th Cir.2011) (alterations in original) (quoting *United States v. U.S. Infrastructure, Inc.,*576 F.3d 1195, 1203 (11th Cir.2009)). Moreover, the nature of a conspiracy often requires that its existence be proven inferentially or circumstantially from the conduct of the participants. *United States v. Molina,*443 F.3d 824, 828 (11th Cir.2006). “A conspiracy conviction will be upheld ... when the circumstances surrounding a person’s presence at the scene of conspiratorial activity are so obvious that knowledge- of its character can fairly be attributed to him.” *United States v. Mateos,*623 F.3d 1350, 1362 (11th Cir.2010) (alterations in original) (quoting *United States v. Figueroa,*720 F.2d 1239, 1246 (11th Cir.1983)).

The evidence, taken in a light most favorable to the jury’s verdict, is sufficient to establish an illegal agreement among McQueen, Griffin, and others on the night of February 25th to violate the civil rights of numerous inmates at the prison facility. For starters, by many accounts (obviously credited by the jury) McQueen and Griffin joined together to use force and violence against the inmates, not in order to maintain discipline, but as a way of punishing them. The evidence showed that Griffin, in Sergeant McQueen’s presence, beat one inmate around the hands with a broomstick when the inmate refused to offer the name of another prisoner who fought with Woods. Despite McQueen’s obligation to intervene he did nothing. The evidence also revealed that McQueen, in the presence of the other officers, including Griffin, assaulted another inmate — who had been involved in a prison fight — beating him with a broken broomstick and throwing him to the ground, when this prisoner refused to disclose the name of the inmate with whom he had been fighting. Again, *1154neither Griffin nor Dawkins intervened to stop McQueen’s assault.

The evidence further established that the officers, including McQueen and Griffin, sanctioned a prison fight between two of the inmates. The rules of the fight were set by Griffin in the presence of Sergeant McQueen. And when the inmates broke the rules, defendant McQueen beat the inmates in order to compel compliance. McQueen also stood by and did nothing as other corrections officers beat still more inmates. This evidence, likewise, contradicted McQueen’s incident report, which made no mention of the pervasive violence. Thus, the evidence suggests, at a minimum, that McQueen and Griffin gathered in a day room and pummeled various prisoners in tandem, and McQueen sought to hide the incident from his superiors despite his plain duty to inform them.

C.

At the end of the trial, the appellants asked the district court to give the jury two defense instructions, one concerning accomplices, informers, or immunized witnesses, and the other addressing multiple conspiracies. The court denied both requests; McQueen and Dawkins claim that each error requires a new trial. We are unpersuaded.

We review a district court’s decision to refuse to give a requested jury instruction for abuse of discretion. *United States v. Condon,*132 F.3d 653, 656 (11th Cir.1998) (per curiam). Criminal defendants may request that the court instruct the jury about their theory of defense “separate and apart from instructions given on the elements of the charged offense” if “there has been some evidence adduced at trial relevant to that defense.” *United States v. Ruiz,*59 F.3d 1151, 1154 (11th Cir.1995). McQueen and Dawkins’s first assignment of error fails because they presented no evidence that the corrections officer or inmates who were called to testify were subject to pending disciplinary charges or criminal prosecution, or that any of them received immunity in exchange for testimony, or finally that any were paid to testify. In short, there was no evidence that these witnesses were accomplices, informants, or otherwise immunized.

Moreover, there was no evidence presented in support of a multiple conspiracy charge. The indictment charged a single conspiracy among the correction officers (including Sergeant McQueen) to deprive numerous inmates of their rights to be free from cruel and unusual punishment. The evidence presented supported a finding of a single conspiracy, not multiple conspiracies. The defendants have failed to identify any credible evidence supporting multiple conspiracies. Indeed, the evidence established only that several corrections officers acting in concert beat inmates at SFRC, forced them to fight among themselves, and did nothing as the beatings unfolded.4

*1155D.

Dawkins and McQueen, relying on *United States v. Hilton,*772 F.2d 788 (11th Cir.1985), also claim the government improperly bolstered the credibility of a corrections officer, Shalisa Rolle. We disagree.

In the first place, it’s not at all clear to us that the prosecutor improperly bolstered Rolle’s testimony. On direct examination she testified that she did not initially disclose the events of February 25th to the investigators because she didn’t want to get involved. She then explained that she told the FBI what she knew only after they told her they were going to polygraph her and that she could face ten years in jail. Defense counsel also inquired about Rolle being threatened by the FBI. Throughout her examination Rolle made it clear that she was never polygraphed. Then, on re-direct examination, the prosecutor asked the witness if she eventually told the truth because she would have flunked a polygraph test if she took it. The defendants objected and sought a mistrial; the district court overruled the objection and denied the motion for a mistrial, reasoning that Rolle never took a polygraph test. Rather, she was threatened with one.

*Hilton*is inapposite, because unlike in *Hilton,*Rolle never indicated that she was willing to take a polygraph test and never did so. Her testimony was not bolstered in any way by the view that the witness had some extra indicia of credibility because of her willingness to be polygraphed. Nor, unlike the circumstances found in *Hilton,*was Rolle testifying pursuant to the terms of a plea agreement. There was, in short, nothing suggesting to the jury that the prosecutor possessed some form of extrinsic evidence never shown to the jury that convinced the prosecution the defendants were guilty.

But even if we assume there was error, the error would warrant a reversal only if it “affected the substantial rights of the defendants.” *Hilton,*772 F.2d at 786; *see also United States v. De La Cruz Suarez,*601 F.3d 1202, 1218 (11th Cir.2010) (“[P]rosecutorial ■ misconduct, such- as vouching, is ‘a basis for reversing an appellant’s conviction only if, in the context of the entire trial in light of any curative instruction, the misconduct may have prejudiced the substantial rights of the accused.’” (quoting *United States v. Lopez,*898 F.2d 1505, 1511 (1990))). “A defendant’s substantial rights are prejudicially affected when a reasonable probability arises that, but for the remarks, the outcome of the trial would be different.” *Id.*(quoting *United States v. Hall,*47 F.3d 1091, 1098 (11th Cir.1995)). The appellants cannot meet this burden.

Rolle’s testimony was minor. She testified that she saw the prisoners in the day room and that two inmates were preparing to fight as the Corrections Officers stood by. But this testimony duplicates the testimony of seven other witnesses. Moreover, Rolle did not discuss the wanton violence inflicted on the inmates by Griffin and McQueen — facts presented by several eyewitnesses. Given the overwhelming and repeated evidence of the beatings and the multiple acts of concealment, we have little difficulty in concluding that any claimed error did not affect the defendants’ substantial rights. *See United States v. Cano,*289 F.3d 1354, 1366 (11th Cir.2002).

'III.

Turning to the government’s cross-appeal, the United States argues that the sentencing of McQueen and Dawkins was substantively unreasonable. After thor*1156ough review, we agree, vacate each sentence, and remand for resentencing.

When imposing a sentence, the court is obliged to consider a critical list of penological factors outlined by Congress in 18 U.S.C. § 3553(a). Thus, “[t]he court shall impose a sentence sufficient, but not greater than necessary,” to “reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense”; “to afford adequate deterrence to criminal conduct”; “to protect the public from further crimes of the defendant”; and “to provide the defendant with needed educational or vocational training, medical care, or other correctional treatment in the most effective manner.” § 3553(a). The district court is also required to consider the nature and circumstances of the offense, the kinds of sentences available, the sentencing range established by the Sentencing Guidelines for the applicable category of offense committed by the defendant, pertinent policy statements, the need to provide restitution, and the need to avoid sentencing disparities among similarly situated defendants. *Id.*

It is abundantly clear that the district courts have 'institutional advantages in applying and weighing § 3553(a)’s factors in individual cases. *United States v. Pugh,*515 F.3d 1179, 1190-91 (11th Cir.2008). Plainly, these advantages afford the district court the best opportunity to sentence individual defendants, and to tailor the sentence with the necessary particularity; consequently, the trial courts are granted very broad discretion when imposing sentences. *Id.*at 1191. In the face of this discretion, it is only the rare sentence that will be substantively unreasonable. But the district courts’ discretion is not unbridled; “[l]ooking at sentencing decisions through the prism of discretion is not the same thing as turning a blind eye to unreasonable ones.” *United States v. Irey,*612 F.3d 1160, 1191 (11th Cir.2010) (en banc). The Supreme Court has made it abundantly clear that, in reviewing sentences, the appellate courts are obliged to remand for resentencing if left with the definite and firm conviction that the district court arrived at a sentence falling outside the range of reasonable sentences. *See Gall v. United States,*552 U.S. 38, 46, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007); *see also Irey,*612 F.3d at 1188. As we wrote in *Pugh:*

> [A]n appellate court may still overturn a substantively unreasonable sentence, albeit only after examining it through the prism of abuse of discretion, and ... appellate review has not been extinguished. Thus, a sentence still may be substantively unreasonable if it does not achieve the purposes of sentencing stated in § 3553(a). So, even though we afford due deference to the district court’s decision that the § 3553(a) factors, on a whole, justify the extent of the variance, we may find that a district court has abused its considerable discretion if it has weighed the factors in a manner that demonstrably yields an unreasonable sentence. We are therefore still required to make the calculus ourselves, and are obliged to remand for resentencing if we are left with the definite and firm conviction that the district court committed a clear error of judgment in weighing the § 3553(a) factors by arriving at a sentence that lies outside the range of reasonable sentences dictated by the facts of the case.

515 F.3d at 1191 (citations omitted) (internal quotation marks omitted).

Moreover, our review for substantive reasonableness is not limited to the factors examined by the district court. Section 3553(a) “sets forth numerous factors that guide sentencing,” and those *1157factors “guide appellate courts ... in determining whether, a sentence is unreasonable.” *United States*v.. *Booker,*543 U.S. 220, 261, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). Indeed, a sentence may be unreasonable if it is grounded solely on one factor, relies on improper factors, or ignores relevant factors. *Pugh,*515 F.3d at 1194. Here, after balancing the factors, we are left with the definite, and firm conviction that the district court arrived at two unreasonable sentences and in the process abused its considerable discretion.

The sentences in this case are substantively unreasonable because they are wholly insufficient to achieve the purposes of sentencing set forth by Congress in § 3553(a). For starters, the sentences of McQueen and Dawkins completely fail to “reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense.” 18 U.S.C. § 3553(a)(2)(A). As described in the legislative history of § 3553(a)(2)(A):

> This purpose — essentially the “just deserts” concept — should be reflected clearly in all sentences; it is another way of saying that the sentence should reflect the gravity of the defendant’s conduct. From the public’s standpoint, the sentence should be of a type and length that will adequately reflect, , among other things, the harm done or threatened by the offense, and the public interest in preventing a recurrence of the offense.

S.Rep. No. 98-225, at 75-76 (1983), *reprinted in*1984 U.S.C.C.A.N. 3182, 3258-59. “Because the punishment should fit the crime, the more serious ,the criminal conduct is the greater the need for retribution and the longer the sentence should be.” *Irey,*612 F.3d at 1206.

The appellants’ actions as corrections officers were particularly serious. McQueen’s conduct as a ranking law enforcement officer was egregious. He was a sergeant then in charge of the youthful offender wing of the South Florida Reception Center on the night of February 25th. He wantonly attacked a young and injured prisoner with a' broken broomstick and slammed the prisoner (face first) when the inmate refused to answer the officers’ questions. The force of the slam aggravated the gash on the already wounded prisoner.' He forced two other prisoners to box and slapped and choked them when they did not fight to his liking. McQueen choked Pressley, causing Pressley to beg for the fight’s end, all to no avail. And McQueen struck at least three other young inmates with part of a broomstick — a dangerous weapon — leaving welts and bruises that remained days after the beatings. To cover his tracks, McQueen filed a false report, lied about the injuries suffered by inmate Woods, and failed to mention the physical abuse sustained by several of the prisoners. McQueen also sat idly by as other inmates were beaten by still other corrections officers for no legitimate reason even remotely related to maintaining order and discipline. Moreover, Dawkins also helped to conceal this brutal behavior. Despite having a duty to report McQueen’s actions, co-defendant Dawkins likewise failed to inform anyone about the repeated beatings and, in fact, filed a flagrantly false report that failed to mention any of the violence that pervaded the youthful offender wing on February 25, 2009.

A violation of Title 18 U.S.C. § 241 is a particularly serious offense. Sections 241 and 242 “are companion sections designed for the protection of great rights won after the Nation’s most critical internal conflict.” *United States v. Williams,*341 U.S. 70, 87, 71 S.Ct. 581, 95 L.Ed. 758 (1951) (Douglas, J., dissenting). Congress passed § 241 during a tumultuous time in our history *1158and thought the statute critical. As the Supreme Court has said,

> Section 241 was enacted as part of what came to be known as the Enforcement Act of 1870. The Act was passed on May 31, 1870, only a few months after ratification of the Fifteenth Amendment. ... Between 1866 and 1870 there was much agitated criticism in the Congress and in the Nation because of the continued denial of rights to Negroes, sometimes accompanied by violent assaults. In response to the demands for more stringent legislation Congress enacted the Enforcement Act of 1870.... [I]t included § 241 in the Act using broad language to cover not just the rights enumerated in § 242, but all rights and privileges under the Constitution and laws of the United States.

> ... It is clear, therefore, that § 241, from original enactment through subsequent codifications, was intended to deal, as Mr. Justice Holmes put it, with conspiracies to interfere with “Federal rights, and with all Federal rights.”

*United States v. Price,*383 U.S. 787, 801-03, 86 S.Ct. 1152, 16 L.Ed.2d 267 (1966) (footnotes & citations omitted). Congress fully understood the importance of protecting citizens from the abuses of official power. *See id.*at 819, 86 S.Ct. 1152 (“I believe that the United States has the right, and that it is an incumbent duty upon it, to go into the States to enforce the rights of the citizens against all who attempt to infringe upon those rights when they are recognized and secured by the Constitution of the country.” (quoting Cong. Globe, 41st Cong., 2d Sess., 3611-3613 (1870) (remarks of Sen. Pool))). The evils against which this civil rights statute is directed especially include correctional officers who flagrantly beat inmates (and young ones at that) placed by the law in their charge. *See Farmer v. Brennan,*511 U.S. 825, 834, 114 S.Ct. 1970, 128 L.Ed.2d 811 (1994) (“Being violently assaulted in prison is simply not part of the penalty offenders pay for their offenses against society.” (internal quotation marks omitted)).

In the second place, these sentences wholly fail to adequately deter criminal conduct. 18 U.S.C. § 3553(a)(2)(B). Plainly, “[g]eneral deterrence ... is one of the key purposes of sentencing.” *United States v. Medearis,*451 F.3d 918, 920-21 (8th Cir.2006); *see also*S.Rep. No. 98-225, at 75-76, 1984 U.S.C.C.A.N. at 3259 (“to deter others from committing the offense” is one of the four purposes of sentencing). The need for the criminal law to deter seems especially compelling here. Prison inmates serve them sentences under the pervasive control of the corrections staff. “Prisoners are uniquely vulnerable to officials who control every aspect of their lives.... ” *Maryland v. Shatzer,*559 U.S. 98, 127, 130 S.Ct. 1213, 175 L.Ed.2d 1045 (2010) (Stevens, J., concurring). Indeed, they may turn only to corrections officers for protection from beatings by other inmates, let alone from punitive beatings sustained at the hands of the officers themselves.

Moreover, violent abuse by corrections officers against inmates may easily go undetected and unpunished. The facts adduced at trial fully bear this out: of some two dozen prisoners who saw the gross violation of the constitutional rights of many prisoners, only one spoke out. The other inmates remained silent in fear of reprisal and, indeed, in some cases even lied to prison officials during the investigation, telling the officials they saw nothing. The fear of retaliation from Griffin, McQueen, and other corrections officers was palpable and well founded. The ability to unearth these crimes by law enforcement officers in a prison setting is particularly difficult, and, as we see it, the *1159extraordinarily lenient sentences in this case sap the goal of general deterrence. *Cf. United States v. Engle,*592 F.3d 495, 502 (4th Cir.2010).

We add that obstruction of justice is a crime that Congress also has aggressively sought to deter. When it passed § 1519 in 2002, the Senate concluded that “[t]he intent of the provision is simple; people should not be destroying, altering, or falsifying documents to obstruct any government function.” S. Rep. 107-146 at 15. Section 1519 was meant to close loopholes in the criminal law relating to the destruction or fabrication of evidence and to counteract the narrow reading by courts of other obstruction laws. *Id.*at 14. The law was 'meant to provide for criminal prosecution and enhanced penalties for those who altered or destroyed evidence. 148 Cong. Rec. S7350 (daily ed. July 25, 2002) (remarks of Sen. Kerry). The § 1519 convictions in this case are particularly serious because the obstructions of justice were intended by law enforcement officers to conceal the repeated physical abuse of many inmates at their own hands.

In the third place, the sentences imposed on McQueen and Dawkins fall far below the sentencing range that the Guidelines have established. 18 U.S.C. § 3553(a)(4). While the Guidelines range is advisory, “consideration of the advisory guidelines range is important.” *Irey,*612 F.3d at 1217. The Sentencing Guidelines recommended a sentence of at least one-hundred-and-fifty-one months for McQueen and a sentence of at least fifteen months for Dawkins; yet the district court dramatically lowered the sentences for both of them. McQueen was sentenced to twelve months’ imprisonment, a drop of one-hundred-and-thirty-nine months and a reduction of some 92% from the bottom of his Guidelines range. And Dawkins was sentenced only to one month in prison, a drop of 93% from the low end of his recommended sentence. By any fair measure, these are “major” variances. *See Irey,*612 F.3d at 1196 (characterizing 42% variance as major). “Although there is no proportionality principle in sentencing, a major variance does require a more significant justification than a minor one — the requirement is that the justification be ‘sufficiently compelling to support the degree of the variance.’ ” *Id.*(quoting *Gall v. United States,*552 U.S. 38, 50, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)). As we see it, the district court offered no reasoned justification other than that Griffin was getting a lower sentence. While that alone may be enough for some variance, it cannot alone account for dramatic variances of over 90% for both defendants under the peculiar facts of this sad case.

The district court viewed the “need to avoid unwarranted sentence disparities among defendants with similar records who have been found guilty of similar conduct” as critical. 18 U.S.C. § 3553(a)(6). It focused on a perceived disparity of sentences between Griffin on the one hand and Dawkins and McQueen on the other. The district court concluded that Dawkins and McQueen were “similarly situated” to Griffin, but that conclusion is not at all clear to us. McQueen was found guilty by a jury of feloniously violating several criminal statutes — 18 U.S.C. § 241 and § 1519; and Dawkins was convicted of obstructing justice too. A different jury, which heard evidence specific to Griffin, did not find Griffin guilty of violating anything. It was unable to reach a verdict and a mistrial was declared. Unlike McQueen and Dawkins convictions, Griffin was never convicted by anyone of any felony; rather, he entered a plea agreement, and, most dis-similarly from McQueen and Dawkins, his crime of conviction was only a misdemean- or. *See United States v. Jayyousi,*657 *1160F.3d 1085, 1117-18 (11th Cir.2011) (noting a court unreasonably failed to consider “significant distinctions” between defendants and criminal defendants sentenced by other courts who were. convicted of “less serious” offenses).

Moreover, the need to avoid unwarranted sentencing disparity also requires the court to consider other similarly situated defendants — criminal defendants in other cases who were convicted of similar crimes. *See Pugh,*515 F.3d at 1202. As best as we can tell, the federal courts have treated violations of § 241 by police or corrections officers as serious crimes meriting far higher sentences than the sentences issued here. *See, e.g., United States v. Gilpatrick,*548 F.3d 479, 481-82 (6th Cir.2008) (affirming one-hundred-and-eight months’ imprisonment where corrections officer convinced inmates to attack other prisoner); *United States v. Owens,*437 Fed.Appx. 436, 438 (6th Cir.2011) (affirming sixty-three months’ imprisonment for officer who violated § 241); *United States v. Lopresti,*340 Fed.Appx. 30, 31 (2d Cir.2009) (noting fifty-one months’ imprisonment for corrections officer who assaulted inmate in violation of § 241, and who made false statements in violation of 18 U.S.C. § 1001). And courts have imposed sentences far higher than a single month of imprisonment to law enforcement officers convicted- of obstructing justice in violation of § 1519. *See, e.g., Fontenot,*611 F.3d at 736 (noting sentence of fifteen months where corrections officer lied on report to cover illegal use of force on inmate); *United States v. Jackson,*186 Fed.Appx. 736, 738 (9th Cir.2006) (affirming sentence of twenty-four months’ imprisonment where agent omitted facts from report). To be sure, courts have at times given sentences below the minimum suggested by the Guidelines. *See, e.g., United States v. Hunt,*526 F.3d 739, 746 (11th Cir.2008) (finding downward departure of five months reasonable for § 1519 violation); *Owens,*437 Fed.Appx. at 438 (affirming § 241 sentence of sixty-three months where the Guidelines suggested eighty-seven months); *United States v. Carroll,*189 Fed.Appx. 450, 455-56 (6th Cir.2006) (affirming § 241 sentence of fifty-one months where Guidelines suggested range of fifty-seven to seventy-one months). But those cases gave more-tempered reductions, and neither McQueen nor Dawkins has cited a similar case in which a federal court has granted so substantial a variance in sentence for law enforcement officers engaged in this kind of predatory conduct. Nor can we find a single case .with sentences remotely as low as those received by McQueen or Dawkins for their respective violations. By imposing these sentences, the district court helped create the very unwarranted disparities it sought to avoid. *See Pugh,*515 F.3d at 1203.

Thus, taking the § 3553(a) factors as a whole as well as the district court’s findings, we can only conclude that McQueen’s and Dawkins’s sentences were substantively unreasonable and that the district court abused its considerable discretion in imposing them. Undoubtedly, a district court has great discretion in balancing the § 3553(a) factors. Still, it must afford “some weight to the factors in a manner that is at least loosely commensurate with their importance to the case, and in a way that ‘achieve[s] the purposes of sentencing stated in § 3553(a).’ ” *Id.*(alteration in original) (quoting *United States v. Martin,*455 F.3d 1227, 1237 (11th Cir.2006)). If a district court instead commits a clear error of judgment in weighing the sentencing factors and arrives at a sentence beyond the range of reasonable sentences, we are duty bound to vacate and remand for resentencing. *United States v. McBride,*511 F.3d 1293, 1297-98 (11th *1161Cir.2007) (per curiam). As we see it, the trial court focused virtually exclusively on one factor — unwarranted disparities — to the near abandonment of other critical factors and arrived at sentences falling profoundly outside the range of reasonable sentences.

Accordingly, we vacate the sentences imposed on McQueen and Dawkins and remand to the district court for further review and resentencing. In so doing we do not suggest what the sentence should be; nor do we intimate that no variance is justified. We simply hold that downward variances of more than 90% where one corrections officer brutalized more than five young prisoners and then lied about it, and another intentionally sought to conceal these serious crimes are unreasonable.

AFFIRMED in part, VACATED in part, and REMANDED for further proceedings consistent with this opinion.

1

. The PSI recommended adjusting the offense level upward by two levels because Dawkins "abused a position of public or private trust ... in a manner that significantly facilitated the commission or concealment of the offense.” U.S.S.G. § 3B1.3. Both parties agreed, however, that Dawkins did not abuse a position of trust, so his offense level remained at 14.

2

. The appellants raise still other arguments, but we find no merit in any of them. Dawkins maintains that the government introduced no evidence establishing a duty to report fights in the housing unit logs. But a corrections officer, two captains, and an inspector unambiguously testified that corrections officers must report *any*incident of violence, whether between prisoners or between a prisoner and a corrections officer. The jury heard sufficient evidence from which it could reasonably find that Dawkins knew he was supposed to record incidents of inmate fighting, an officer's use of force, *and*injuries sustained by inmates in the log, and the defendant knowingly failed to comply with these requirements.

Dawkins and McQueen also marshal a cumulative-error argument; that their Confrontation Clause rights were violated, that the district court unduly limited cross-examination, that the court allowed the introduction of hearsay evidence, and that the rule of witness sequestration was violated. Most of the alleged errors were, not errors at all. Thus, for example, the Confrontation Clause argument asserts that photographs of the *victim*inmates were introduced without giving Dawkins and McQueen an opportunity to confront the inmates. But the photographs were introduced through the testimony of a corrections officer, who testified that the photographs accurately depicted the bruises and welts he saw on the inmates after the attack. Dawkins and McQueen had every opportunity to cross-examine this witness. Their argument that the district court unduly limited cross-examination is unfounded. Our review of the record reveals that the district court gave the defendants ample opportunity to cross-examine all the witnesses, and Dawkins and McQueen have failed to offer a single example of the' court having improperly restricted them. Likewise, the district court did not abuse its discretion in refusing to grant a mistrial as a result of the violation of the rule of witness sequestration. The district court allowed McQueen and Dawkins to cross-examine the witnesses about any improper interaction, a remedy that we have approved of in all but the most egregious of cases. *United States v. Blasco,*702 F.2d 1315, 1326-27 (11th Cir.1983). To the extent any of the district court's rulings were erroneous, none had a substantial influence on the outcome of the case, *see United States v. Jones,*601 F.3d 1247, 1262 n. 6 (11th Cir.2010), and the cited *errors even when*taken together did not affect Dawkins’s or McQueen’s substantial rights, *United States v. Ladson,*643 F.3d 1335, 1342 (11th Cir.2011).

3

. Fifth Circuit decisions issued before the close of business on September 30, 1981 are binding precedent in the Eleventh Circuit. *See Bonner v. City of Prichard,*661 F.2d 1206, 1209 (11th Cir.1981) (enbanc).

4

. McQueen also contests the jury instructions for supposedly saying he could "be found guilty of conspiracy against rights through deliberate indifference." According to him, § 241 is a specific intent crime, and the jury instruction did not reflect this. This argument fails too because the district court explicitly instructed the jury on specific intent: "The defendants can be found guilty of [conspiracy against rights] only if all of the following facts are proved beyond a reasonable doubt: First, a conspiracy existed, that is, two or more persons in some way agreed to try to accomplish a shared and unlawful plan *with specific intent to deprive inmates*at the South Florida Reception Center of the right to be free from cruel and unusual punishment."