
502 F.3d 425 (2007)
UNITED STATES of America, Plaintiff-Appellee,
v.
James Wendell ROACH (06-6266/6564) and Patrick James Sheldon (06-6298), Defendants-Appellants.
Nos. 06-6266, 06-6298, 06-6564.
United States Court of Appeals, Sixth Circuit.
Argued: July 27, 2007.
Decided and Filed: September 11, 2007.
*428 ARGUED: Nikki C. Pierce, Federal Defender Services, Greeneville, Tennessee, S. Joanne Sheldon, Newport, Tennessee, for Appellants. M. Neil Smith, Assistant United States Attorney, Greeneville, Tennessee, for Appellee. ON BRIEF: Nikki C. Pierce, Tim S. Moore, Federal Defender Services, Greeneville, Tennessee, S. Joanne Sheldon, Newport, Tennessee, for Appellants. M. Neil Smith, Assistant United States Attorney, Greeneville, Tennessee, for Appellee.
Before: GILMAN and GRIFFIN, Circuit Judges; ACKERMAN, District Judge.[*]

OPINION
RONALD LEE GILMAN, Circuit Judge.
In 2006, a jury convicted former Newport, Tennessee Police Officer James Wendell Roach of depriving two Hispanic men of their civil rights under color of law, in violation of 18 U.S.C. § 242, and convicted former Newport, Tennessee Police Officer Patrick James Sheldon of being an accessory after the fact, in violation of 18 U.S.C. § 3. Roach was sentenced to 10 months of imprisonment and Sheldon was given two years of probation. The district court also denied Roach's motion for bond pending appeal. For the reasons set forth below, we AFFIRM both the judgment of the district court and its denial of Roach's motion for release on bond.

I. BACKGROUND

A. Factual background
Roach and Sheldon were both sergeants with the Newport, Tennessee Police Department. While on patrol on Saturday, March 12, 2005, at approximately 5:20 p.m., they allegedly stopped, without probable cause, a van driven by Wilder Gomez Roblero (Gomez). Marcos Mejia Vasques (Mejia) was a passenger in the van. Both men were illegal aliens. During the stop, Roach allegedly took five twenty-dollar bills from Mejia's wallet and additional money from Gomez's wallet. He then purportedly ordered the men on their way before either Mejia or Gomez discovered the loss. No traffic citations were issued as a result of the stop.
On the afternoon in question, Gomez and Mejia were driving in Gomez's minivan to the Wal-Mart in Newport. Gomez had a cell phone with him in the car. He received a phone call not long after he and Mejia left Gomez's home. A few minutes later, as Gomez drove toward the intersection *429 of Mineral Street and Woodlawn Avenue in Newport, Gomez was pulled over by what he described as a black-and-white police car. The police car did not have a light-bar on its roof; instead, its blue lights were inside the car.
Two police officers emerged, one approaching each side of the minivan. The officer on Mejia's side of the van was wearing sunglasses. Mejia was ordered out of the van, frisked, and his wallet inspected. Gomez testified that the officer on his side of the minivan was more polite, and asked for his driver's license. The officer then ordered Gomez out of the vehicle, and directed him to the passenger side where he was also frisked and his wallet taken from his pocket. Gomez's wallet was returned to his pocket and he was directed to leave. As Gomez and Mejia drove away, Mejia opened his wallet and discovered that money had been taken. Gomez testified that money was missing from his wallet as well. The men then drove from the traffic stop to Gomez's house, where Gomez's wife suggested that they report the theft to Maria De La Cruz, an acquaintance who worked as a translator for the Cocke County, Tennessee Health Department.
Gomez called De La Cruz on his cell phone, but her number rang busy. He called again shortly thereafter and spoke with her. She, in turn, called 911 and spoke with a dispatcher about the incident. A Newport Police Department supervisor later contacted De La Cruz to say that Gomez and Mejia would need to speak with the Chief of Police, Maurice Shults, on the following Monday if they wished to pursue their complaint.
Gomez and Mejia, accompanied by De La Cruz, met with Shults on that Monday. Shults asked Gomez and Mejia to view a photo array of officers with the Newport Police Department on his computer. Mejia was unable to identify the officer who had come to his side of the van. Gomez, however, identified Sheldon as the officer who came over to the driver's window. Shults also asked the men to look at the department's patrol cars and to identify the car that had stopped them. Gomez and Mejia identified Unit 18, the only black-and-white patrol car without a light-bar on its roof (thus referred to as a "slick-top"). Unit 18 also lacked an in-car video recording system. Sheldon and Roach had been assigned to Unit 18 at the time of the incident. Shults then contacted the Tennessee Bureau of Investigation (TBI) and asked it to take over the inquiry.
TBI Special Agent Geoff King interviewed Sheldon about Gomez's and Mejia's complaint on Monday, March 14, 2005. Sheldon denied that he and Roach had stopped any Hispanics on the day of the alleged incident. Instead, he recounted that he and Roach had been at the By-Lo Grocery in Newport at the time that Gomez and Mejia claimed the stop had occurred. After leaving the grocery, Sheldon told King that a woman whose car had been vandalized flagged down his patrol car. Roach and Sheldon then conducted a traffic stop of Roy Maples, whom they believed to be driving with a revoked or suspended license, a stop that was documented as occurring at 5:35 p.m.
King also interviewed Michael Gray, an emergency medical technician who worked for Allied Emergency Medical Service, a private ambulance company. Allied had a station house at the intersection of Jones Circle and Mineral Street in Newport. Gray was on duty on the day of the alleged stop. Sometime between 5:00 and 6:00 p.m. on March 12, 2005, Gray was washing his personal vehicle outside the station house. He observed a Newport Police Department patrol car pull over a dark-colored minivan across the street from the *430 Allied station. Gray further testified that he recognized the officers in the car as Roach and Sheldon. The driver of the van, according to Gray, was a dark-skinned Hispanic man. Gray went back inside the station house before the vehicles left. After speaking with Gray, King again interviewed Sheldon. King reviewed Sheldon's previous statement and then asked if there was anything that Sheldon wished to add or change about the information that he had provided. Sheldon declined to make any changes or additions.
King then interviewed Roach. Like Sheldon, Roach denied stopping Gomez and Mejia, or any other Hispanic individuals, on the day in question. Roach instead told King that he and Sheldon had left the police station some time after 5:00 p.m., drove to Wal-Mart and stayed inside for approximately twenty minutes, then drove to the By-Lo Grocery, where they stayed for another 30 or 40 minutes. After leaving the grocery, Roach said that he and Sheldon were flagged down by a woman whose car had been vandalized. Their next action, according to Roach, was the traffic stop involving Roy Maples.
At trial, Chief Shults testified that the driving time from the police station to the Wal-Mart was approximately six minutes, and the driving time from the Wal-Mart to the Allied EMS station house was approximately four minutes. This testimony demonstrated that Roach and Sheldon would have been able to conduct the traffic stop of Gomez and Mejia at 5:20 p.m. and still have been able to conduct the traffic stop of Roy Maples at 5:35 p.m. Furthermore, TBI Agent King said that the time line of events given by Roach and Sheldon was contradicted by surveillance-camera photos taken at Wal-Mart, which showed the officers entering the store shortly before 5:00 p.m. and leaving approximately three minutes later.
Kathy Cody, the director of Cocke County 911, also testified at trial and introduced a recording of telephone and radio traffic with police officers that was made on March 12, 2005. The recording indicated that Sheldon had called in a license plate for identification at approximately 5:26 p.m. as part of the Roy Maples traffic stop. But Cody testified that the time-stamps on the recording were approximately nine minutes behind the actual time that the events occurred, a discrepancy that she discovered only upon making the recording for the TBI investigators. Accordingly, the actual time that Sheldon placed the license plate identification request was approximately 5:35 p.m. The police telephone and radio traffic recording contained no calls from Sheldon or Roach prior to the Roy Maples stop. In contrast, the recording confirmed that De La Cruz had called the dispatcher to report the alleged theft at approximately 5:44 p.m. (actual time) on March 12, 2005.
Gomez's coworker Sandra Boles testified that she had loaned Gomez an extra cell phone on her cell-phone account and that he paid her for the calls that he made when she received her phone bill. She also said that Gomez had called her on Sunday, March 13, 2005, and told her that he and Mejia had been robbed by two policemen. Gomez, in turn, testified that he remembered receiving a call on the borrowed cell phone soon after leaving home on the afternoon of the alleged traffic stop.
The government introduced evidence of Boles's cell phone records through the testimony of Autumn Click, a Verizon representative. Click testified that Gomez had received calls at 5:18 p.m. and 5:20 p.m. on March 12, 2005, and that the phone had been used to place a call to De La Cruz's home phone at 5:37 p.m.


*431 B. Procedural background
Roach and Sheldon were initially charged in a three-count indictment with depriving Gomez (Count II) and Mejia (Count III) of their civil rights under color of law in violation of 18 U.S.C. § 242, and with conspiracy to do the same in violation of 18 U.S.C. § 241 (Count I). Both defendants filed motions to dismiss the indictment, alleging that the government had violated their Fifth, Sixth, and Fourteenth Amendment rights by sending agents with the Federal Bureau of Investigation (FBI) to interview a translator working with the investigator hired by defense counsel. Following an evidentiary hearing on the motions, the assigned magistrate judge recommended that the district court deny the motions as meritless. The district court held a hearing on the defendants' objections to the magistrate judge's Report and Recommendation. In a subsequent written order, the district court adopted the recommendation of the magistrate judge and denied the motions to dismiss the indictment.
The trial commenced on February 2, 2006. Deliberations by the jury began on the afternoon of February 7, 2006. On February 8, 2006, the jury returned a verdict of not guilty as to the conspiracy count against both defendants. The district court then instructed the jurors to return the following morning to continue deliberations as to the remaining counts of the indictment. When the jury indicated on February 9, 2006 that it was deadlocked, the district court declared a mistrial as to the deprivation-of-civil-rights counts against Roach and Sheldon. A new trial was set for March 21, 2006.
On February 14, 2006, the grand jury returned a superseding indictment against Roach and Sheldon. The superseding indictment again charged both officers with depriving Gomez (Count I) and Mejia (Count II) of their civil rights under color of law, omitted the conspiracy charge, and charged Sheldon with being an accessory after the fact (Count III). Roach and Sheldon filed a joint motion to dismiss the superseding indictment's civil rights charges. Sheldon also filed a separate motion to dismiss the new accessory charge directed solely against him. Finally, the defendants jointly filed a motion in limine, alleging government intimidation of prospective defense witness Charles "Mo" Swanson. After a hearing on all three motions, the district court denied the motions to dismiss and deferred a ruling on the motion in limine.
The second trial began on April 5, 2006 and lasted three days. Immediately before opening statements in the second trial, the district court heard additional arguments on the defendants' allegation of government intimidation. Counsel for the defendants contended that the government was gathering information about unspecified prior bad acts by Swanson for the purpose of bringing charges against him if he testified on behalf of Roach and Sheldon. Although Swanson was not present, his counsel related to the court that Swanson had been told that the government was interviewing confidential informants about his background. Counsel for Swanson also asserted that Swanson had learned that one of his employees, who had quit unexpectedly a week earlier, was a government "plant." Roach and Sheldon asked the court to grant Swanson immunity from prosecution for any prior unspecified acts. The court, finding no evidence of prosecutorial misconduct, refused. Swanson was never called to testify.
Jury deliberations in the second trial began on April 10, 2006 at 2:45 p.m. After less than three hours, the jury sent a message to the district court indicating *432 that it was having difficulty reaching a verdict. The court directed the jurors to continue deliberating the following morning. On April 11, 2006, the jury deliberated from 9:00 a.m. until 12:00 p.m., took a break for lunch, then resumed deliberations at 1:15 p.m. The court received a second message from the jury at approximately 2:30 p.m., again indicating that it was having trouble reaching a verdict and "honestly seem[ed] to be at an impasse." After consulting with counsel for the parties, the court then gave the jury an Allen charge, directing them to continue deliberating. An Allen charge is a "supplemental instruction designed to encourage the jury to reach a verdict by requesting each juror to reconsider his or her respective position during continued deliberations. The name comes from Allen v. United States, 164 U.S. 492, 17 S.Ct. 154, 41 L.Ed. 528 (1896), where the Supreme Court approved such an instruction." United States v. Frost, 125 F.3d 346, 373 (6th Cir.1997). The jury finally returned a verdict on April 12, 2006 at 10:35 a.m., finding Roach guilty of depriving Mejia of his civil rights under color of law (Count II) and finding Sheldon guilty of being an accessory after the fact (Count III).
Roach and Sheldon filed a joint motion for a new trial, alleging prosecutorial misconduct and prosecutorial vindictiveness. The district court denied the motion. Sentencing hearings were then held on September 11, 2006. Roach received a sentence of 10 months of imprisonment, followed by one year of supervised release that included a requirement that he perform at least 100 hours of community service. Sheldon received a sentence of two years' probation with a special condition that he serve two months of that time in intermittent custody. Both defendants filed timely notices of appeal.

II. ANALYSIS

A. Prosecutorial misconduct
Roach and Sheldon raise several claims of prosecutorial misconduct that allegedly require that their convictions be vacated. In his brief, Sheldon adopted the statement of issues presented by Roach "in that they are equally applicable to . . . Sheldon," and instead briefed separate arguments that applied only to Sheldon. Roach contends, for his part, that he was denied a fair trial because (1) the government's rebuttal closing argument improperly argued facts not in evidence and appealed to ethnic and religious prejudices, and (2) federal investigators interviewed the translator working with the defense counsel's investigator prior to trial and improperly asked the translator about the defense's trial strategy.
We evaluate claims of prosecutorial misconduct using a two-step inquiry. "First, the court must determine if the government's statements were improper." United States v. Abboud, 438 F.3d 554, 584 (6th Cir.2006). If we determine that the statements were in fact improper, then we "must decide whether the statements were flagrant." Id. The "flagrancy inquiry" involves four factors:
(1) whether the remarks tended to mislead the jury or to prejudice the accused [including whether the trial judge gave an appropriate cautionary instruction to the jury];
(2) whether they were isolated or extensive;
(3) whether they were deliberately or accidentally placed before the jury; and
(4) the strength of the evidence against the accused.
Id. (citation omitted).
If we determine that the statements were not flagrant, then "the [c]ourt *433 will reverse only if (1) the proof against the defendant was not overwhelming, (2) opposing counsel objected to the conduct, and (3) the court failed to give a curative instruction." Id. (citation and quotation marks omitted). We review such claims de novo where defendants make a timely objection. United States v. Beverly, 369 F.3d 516, 543 (6th Cir.2004). Otherwise, we examine the defendants' claims under the plain-error standard of review. Id.

1. Government's rebuttal closing argument
Roach and Sheldon objected at trial to portions of the government's closing argument. Specifically, they objected to the following allegedly improper statements:
[I]t's not disputed that when Agent King talked to Mr. Gomez and Mr. Mijia [sic], he didn't think to ask them about a cell phone, they didn't think to tell him; but what is telling is Mr. Gomez's testimony. Who was the first person to ask you about the cell phone and ask you, didn't you have a cell phone? It was Mr. Hackett, the investigator for Sergeant Roach; and that's important for one reason, ladies and gentlemen, there were four people on that Saturday afternoon that knew there was a cell phone in that van, Wilder Gomez, Marcos Mijia [sic], Jimmy Roach and Pat Sheldon. That's how they knew to ask. Mr. King didn't ask because he wasn't there at that van that afternoon, but the defense knew to ask about the cell phone because they knew that cell phone was in the van.
. . .
Ms. Pierce [counsel for Roach] asked, Well, you don't even know who Mr. Mijia [sic] and Mr. Gomez are; and that's what they want to make the case about. I think back to the Commandment, thou shalt not steal. It does not say, thou shalt not steal from people you know, thou shalt not steal from citizens, thou shalt not steal from white people.

a. Cell phone comments
In response to the objection of Roach and Sheldon to the government's cell-phone comments, the court cautioned the jury as follows: "[Y]ou've heard the proof. It's for you to decide the facts. If the lawyers misstate the facts, that's up to you to decide."
The defendants assert on appeal that the government's comments about the cell phone in Gomez's car improperly argued facts not in the record. But the primary focus of their argument is that the government's comments necessarily suggested to the jury that the only way that the defense investigator would have known to question Gomez about the borrowed cell phone was if Roach and Sheldon were the officers who made the stop and told the investigator about having seen the cell phone. Furthermore, Roach and Sheldon contend that these comments were "tantamount to a false claim that the defense team was accessories [sic] after the fact to the crime allegedly committed." They claim that the government's argument, when considered in the context of both trials, constitutes reversible error.
The government, on the other hand, contends that its reference to the cell phone was made in response to Roach's own closing argument, in which Roach's counsel stated as follows:
When did they start talking about cell phones? What did they tell you? Only after two months ago, after they testified, did it come up about cell phones. That's important. What they are wanting to do is fix the Gomez/Vasques [sic] problems, and that is that they don't even know when an alleged stop happened.
*434 Sheldon's counsel likewise referred to the cell phone in his closing argument, stating that "Agent King had never heard of the cell phone being thrown or anything until recently."
A review of the evidence offered at the second trial undercuts the defendants' position. Gomez testified that just prior to the traffic stop by Roach and Sheldon, he had received a phone call on the borrowed cell phone. He also testified that a call came in as Roach and Sheldon approached his van during the stop. Although the cell phone was not in Gomez's name, his coworker, Sandra Boles, testified that she had loaned him an extra phone on her cell-phone account and that he paid her for the calls that he made when she received her phone bill. Through the testimony of Boles and of an employee for Boles's cell-phone service provider, the government introduced phone records for the cell phone to corroborate that it was in fact in use at times that were consistent with the government's time line of events for the traffic stop.
The district court considered Roach's and Sheldon's claims that the cell-phone comments constituted reversible error in its denial of their motion for a new trial. Concluding that "[t]he statements by the government attorney during the closing argument were not a misstatement of facts in the record," the court found that "[t]he evidence in the record was simply that the first disclosure of the cell phone came because of a question asked by Hackett." The court determined that the government's argument "was not a misstatement and was certainly a reasonable inference based on the evidence in the record." Moreover, the court found that the defendants had invited the government's argument by making "Gomez'[s] credibility concerning the cell phone an issue in the case in the first place." The court concluded that the comments, even if improper, were not "so pronounced and persistent that [they] permeate[d] the entire atmosphere of the trial," (quoting United States v. Mahar, 801 F.2d 1477, 1503 (6th Cir. 1986)), but rather were confined to "a few short sentences in a lengthy closing made after four days of trial."
Viewed in context, the government's comments about the cell phone constituted approximately five sentences in its rebuttal closing argument. The defendants argue that the statements nonetheless infected the jury's deliberations and thus prevented Roach and Sheldon from receiving a fair trial. To be sure, the government may not rely on prejudicial facts not in evidence when making its closing arguments. United States v. Wiedyk, 71 F.3d 602, 610 (6th Cir.1995). But the evidence tends to support the government's argument in the present case. Gomez testified that the first person to ask him about a cell phone was "a man with a beard," whom he later identified as Brian Hackett, an investigator for the defense. As the district court noted, the record demonstrates that the defendants "vigorously and continually attacked the credibility of the victims" over the course of the entire trial. The government's comments regarding the cell phone and the credibility of Gomez and Mejia, even if not invited, drew a reasonable inference based on the evidence given at the second trial. See United States v. Hickey, 917 F.2d 901, 904 (6th Cir.1990) (concluding that the prosecutor's statement during summation that the defendant was actively involved in drug-dealing was "a permissible argument based on the evidence").
As Roach and Sheldon acknowledge, their defense theory was that they were not the ones who made the traffic stop, if such a stop indeed occurred at all. The government's comments responded to that *435 defense by suggesting that Roach and Sheldon must have made the stop in order for Hackett, their defense investigator, to know to ask Gomez about whether he had a cell phone. On appeal, the defendants contend that the district court's conclusion that they had invited the government's comments essentially punished them for "[t]he presentation of a defense [that] was nothing more than zealous representation of their clients." This conclusory argument ignores the district court's reasoned response to the defendants' motion for a new trial and its analysis of their prosecutorial-misconduct claim.
Roach and Sheldon also raise on appeal what the district court characterized as "the somewhat puzzling argument, without elaboration, that `[t]he government's closing argument is a step beyond making improper comments on a defendant's decision to remain silent, conduct which is prohibited by the Fifth Amendment.'" As the district court properly noted, "[t]he prosecution's statement[s] in this case cannot reasonably be interpreted to have even been an indirect reference to the decision of these defendants to invoke their Fifth Amendment right to remain silent and refuse to testify at trial." We agree with the reasoning of the district court and accordingly adopt its analysis of the defendants' perfunctory Fifth Amendment argument.

b. Religious and ethnic prejudice
Roach and Sheldon further objected to the government's comments during its rebuttal closing argument that the Ten Commandments do not say "thou shalt not steal from white people." This statement, although textually accurate, served, according to the defendants, to incite religious and ethnic bias and thereby deprived them of a fair trial. Roach and Sheldon are both white, whereas Gomez and Mejia are both Hispanic.
A review of the defendants' closing arguments suggests, however, that the government was responding to improper comments made by counsel for Roach. His counsel had argued that
[t]his is one mark in ten years that they're saying on a sergeant; and the whole tale doesn't make any sense. We can't furnish all the answers. We don't know why the Hispanicsthey know how to work the system. They had things to hide. We don't know why this is set up like it is. It's one of the great mysteries; but we know that the government's facts don't work, you can tell from their evidence and their witnesses.
Roach's co-counsel then argued:
What did we learn about the individuals Marcos Mijia [sic] Vasques, Wilder Gomez Roblero? Who are these individuals? That's one question, one of many questions. . . . Who are you? That was a question that was asked by Mr. Smith. Did you hear Mr. Gomez? At first he  there was a big long pause, and he did not want to say who he was. He was also asked his date of birth, and he kept asking, well, which one. He was asked where did he live in New Jersey. I don't remember. For an individual who has come to this country to make a better life, he cannot remember the first place he came to live, this great wonderful country that we live in. Why did he not want to the government to know, us to know, you to know where he lived in New Jersey? Is there more bad things [sic] that he's done out there?
We conclude that the government's statements did not amount to misconduct. The statements were made in response to Roach's closing arguments, which contained inflammatory remarks about Hispanics. Indeed, the district court said in a footnote that defense counsel's statements about Hispanics knowing how to work the *436 system constituted "race-baiting" and were part of a pattern of tactics and statements that the defense had used even more aggressively in the first trial.
To be sure, "[c]ourts universally condemn" the injection of religion into legal proceedings and we do not vary from that condemnation here. Hicks v. Collins, 384 F.3d 204, 223 (6th Cir.2004). But the government's comment was isolated and there is no indication that it misled the jury. The government did not suggest that the jury should decide the case based on theological principles nor make any other reference to religion. Rather, after the defense's objection to the reference to the Ten Commandments, the government continued its closing argument by stating that "[t]he law does not make differences based on who the victim is. Our constitutional rights do not depend on who the victim is. Those rights apply to everyone in the United States."
As the defense points out, there was no contemporaneous cautionary instruction to the jury by the district court. But the defense did not request one either. After the court overruled the defense's objection, there were no further Biblical references during the trial.
In sum, the government's comment, although improper, was not flagrant. Moreover, the comment did not appeal to religious or ethnic prejudice, but was made in response to the inappropriate comments about Mejia and Gomez by the defense. We therefore find no reversible error regarding this issue.

2. Federal investigation of defense translator
Prior to the first trial, Roach and Sheldon filed a motion to dismiss the indictment on the basis that FBI agents had improperly questioned a defense interpreter, Pete Galvez, who worked with the defense investigator, Brian Hackett. Roach and Sheldon contend that the agents questioned Galvez at his home about the defense's legal strategy and inquired into privileged communications. The government responded that it had received a report that Galvez had intimidated Gomez's wife, a witness in the case, in violation of 18 U.S.C. § 1512(b) and (d), and that it accordingly had requested the FBI to inquire into the matter.
A magistrate judge held an evidentiary hearing on the motion to dismiss and heard testimony from Galvez and from the FBI agents who questioned him. In a Report and Recommendation, the magistrate judge found no merit to the defendants' claim and recommended denying their motion. The district court adopted the recommendation over the defendants' objection, finding that the FBI agents properly investigated an alleged threat made to a potential witness, that the defense implicitly waived work-product immunity by calling Galvez to testify about the FBI interview at the evidentiary hearing, and that Galvez had been expressly directed by defense counsel not to go to the Gomez home by himself, but did so nonetheless.
On appeal, Roach focuses on whether defense investigator Hackett was improperly accused of misconduct. The reason for this is not entirely clear. According to the record, Hackett and Galvez jointly visited the Gomez's home on November 11 and spoke with Mrs. Gomez. There was some dispute, however, about whether Hackett was with Galvez when Galvez returned and allegedly intimidated Mrs. Gomez. Roach and Sheldon contend that the incident of alleged intimidation refers to a visit by both Hackett and Galvez. The magistrate judge, however, found that "[a]lthough the proof is very confusing regarding this fact, it appears that six days *437 [after the joint visit to Gomez's home], Galvez returned alone to Mrs. Gomez's house and attempted to talk to her."
Neither Roach nor Sheldon offer any evidence or caselaw that would support their position that the FBI's investigation into whether Galvez allegedly told Mrs. Gomez that he would call the police if she did not open the door to let him in constituted the "functional equivalent of wiretapping and eavesdropping" that prevented the defendants from receiving a fair trial. We likewise find no support for the defendants' argument, and therefore adopt the findings of the magistrate judge and the ruling of the district court denying Roach's and Sheldon's joint motion to dismiss the indictment on this ground.

B. Alleged intimidation of a defense witness
Roach and Sheldon next allege that the district court erred in denying their motion to dismiss the superseding indictment on the ground that the government improperly sought to intimidate a key defense witness. A defendant's right to present his or her own defense witnesses constitutes "a fundamental element of due process." Washington v. Texas, 388 U.S. 14, 19, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967). The right encompasses the Sixth Amendment "right to have compulsory process for obtaining witnesses in [the defendant's] favor." Id. at 19-23, 87 S.Ct. 1920. Prosecutorial and judicial actions aimed at discouraging defense witnesses from testifying may deprive a defendant of this right. See, e.g., Webb v. Texas, 409 U.S. 95, 98, 93 S.Ct. 351, 34 L.Ed.2d 330 (1972) (per curiam) (reversing a conviction where the trial judge severely admonished the sole witness proffered by the defense, who declined to testify as a result); United States v. Thomas, 488 F.2d 334, 336 (6th Cir.1973) (per curiam) (reversing a conviction obtained after a Secret Service agent in an ex parte communication advised a defense witness of possible prosecution if he testified).
Governmental conduct, however, must amount to a substantial interference with a witness's free and unhampered determination to testify before we will find a violation of either due process or the Sixth Amendment. United States v. Pierce, 62 F.3d 818, 833 (6th Cir.1995) (citation omitted) (holding that the government's inappropriate interrogation of a defense witness did not "substantially interfere[] with any free and unhampered determination the witness might have had as to whether to testify"). Even when such interference occurs, a violation of a defendant's right to call witnesses in his or her defense is subject to harmless-error analysis. United States v. Foster, 128 F.3d 949, 953 & n. 4 (6th Cir.1997) (analyzing the standard of review applicable to claims of prosecutorial misconduct based on the alleged intimidation of a defense witness).
In the present case, the defendants argue that the government sought to "chill the presence" of defense witness Charles "Mo" Swanson. This witness allegedly would have testified that Roach and Sheldon were at the By-Lo Grocery, where Swanson was employed, at the time that the traffic stop allegedly occurred. During the first trial, Swanson, who had a prior felony conviction, received a letter from the Tennessee Department of Safety, notifying him that his permit to carry a handgun had been revoked. The letter was carbon-copied to Assistant United States Attorney Neil Smith and to FBI Agent Tom Farrow, who were both on the prosecution team against Roach and Sheldon.
According to the government, the defense had informed the district court during the course of the first trial that it did *438 not intend to call Swanson. The defense raised allegations of witness intimidation for the first time in a motion in limine to dismiss the superseding indictment before the second trial. In response, the government contends that, while investigating the present case, it learned of Swanson's prior federal felony conviction in South Carolina and that he had been issued a license to carry a handgun by the Tennessee Department of Safety. The government notified the Department of Safety by a letter dated January 18, 2006 that Swanson was prohibited under federal law from possessing a handgun. Swanson's permit was revoked the following week.
At a pretrial hearing, the district court heard evidence and argument relating to the defendants' motion to dismiss based on the alleged intimidation of Swanson. The government pointed out that it had not requested the Tennessee Department of Safety to take any action in response to its letter, but rather that it believed that it "had a legal obligation to bring to the attention of the Department of Safety that they had issued a handgun permit in error." When asked by the court why the government could not have waited two weeks until the conclusion of the first trial to communicate with the Department of Safety, the government stated that "every day [Swanson's permit] stood out there uncorrected was another day that that permit had been improperly issued." The court then noted that "the timing of all of this, the letter to the Department of Safety, the Department of Safety's letter to Mr. Swanson, all the timing of all of that is problematic." Moreover, the court stated that it was
confronted with a situation where there's a witness who obviously is very material to these defendants' defenses. This witness puts them somewhere else at the time this alleged offense was occurring or very close to it. A witness who now apparently for whatever reason has come to the conclusion that he's afraid that if he comes into this Court and testifies favorably for these defendants, he may be charged with being a felon in possession of a firearm.
Accordingly, the district court "prohibit[ed] the government from cross-examining Mr. Swanson on any matters related to the alleged possession by him of a firearm while his status was that of a convicted felon." The court also informed the parties that it would wait for the government's decision on whether or not to prosecute Swanson for being a felon in possession of a firearm before making any further decisions on this issue.
Despite noting that a defendant has a Sixth Amendment right to present his or her own witnesses, Washington, 388 U.S. at 19, 87 S.Ct. 1920, the district court issued a written ruling denying the defendants' motion in limine to dismiss on the basis of witness intimidation. Citing Webb, 409 U.S. at 98, 93 S.Ct. 351, the court nonetheless recognized the proposition that "prosecutorial actions aimed at discouraging defense witnesses from testifying may deprive a defendant" of his Sixth Amendment right. One possible remedy for such discouragement would be for the court to grant immunity from prosecution to the witness for the alleged crime uncovered by the prosecutorial actions. United States v. Emuegbunam, 268 F.3d 377, 401 (6th Cir.2001). The court stated that it "ha[d] advised the government that [it] will address this remedy if the government decides that there will be no agreement to not prosecute Swanson."
Although the timing of the government's letter to the Tennessee Department of Safety is highly troubling and AUSA Smith's justification of that timing based on his practice of "tak[ing] care of things *439 as they come across my desk" is questionable, this sequence of events does not establish that Swanson's failure to testify was due to the government's alleged misconduct. Cf. United States v. Foster, 128 F.3d 949, 954 (6th Cir.1997) (finding that the district court should have conducted an evidentiary hearing to determine the effect of the government's misconduct on a defense witness's testimony). The district court in the present case in fact held an evidentiary hearing and inquired extensively into the government's actions and their effect on the witness. Moreover, the court prohibited the government from cross-examining Swanson about his allegedly illegal possession of a gun and indicated that it would be willing to grant Swanson immunity from prosecution on that charge if the government did not waive its discretion to bring charges.
Determining the effect that the government's alleged misconduct had on Swanson was difficult even for the district court, which had the advantage of both physical and temporal proximity to the events. Swanson himself did not appear at the evidentiary hearing, but rather submitted a conclusory affidavit attesting to his fear of negative repercussions should he testify. The court noted that it had authorized a subpoena for Swanson's appearance, but counsel for Roach stated that he had consulted with Swanson's attorney and elected not to serve the subpoena.
There is no allegation that the government threatened to prosecute Swanson for illegally possessing a handgun, although Swanson allegedly felt threatened. The government in fact notified Swanson that it would not prosecute him for any possession of a firearm prior to the date that the Tennessee Department of Safety revoked his handgun permit. Moreover, the court held an extensive hearing immediately prior to opening statements in the second trial and heard arguments from counsel for the defendants, counsel for Swanson, and the government. The defense nonetheless chose not to call Swanson as a witness. Under these circumstances, we conclude that the district court did not err in denying the defendants' motion in limine to dismiss the indictment on the ground of witness intimidation.

C. Allen charge
Roach and Sheldon also contend that the district court erred when it gave the jury an Allen charge after the jury stated that it was having difficulty reaching a verdict. We review a district court's decision to give an Allen charge under the abuse-of-discretion standard. United States v. Cochran, 939 F.2d 337, 340 (6th Cir.1991). The timing of the charge is reviewed under the same standard. United States v. Tines, 70 F.3d 891, 896 (6th Cir.1995). We generally prefer the usage of the Sixth Circuit pattern jury instruction and "its use will, in most instances, insulate a resulting verdict" from challenge on appeal. United States v. Clinton, 338 F.3d 483, 488 (6th Cir.2003).
In the present case, the jury began deliberating at 2:45 p.m. on April 10, 2006. It sent a message to the district court at 5:45 p.m., asking: "What if we are unable to reach a verdict? We don't believe we will be able to reach a verdict tomorrow, either. What should we do? Too much of the evidence is subjective, & minds are fairly well settled." The court declined to instruct the jury further at that time, but asked that the jurors return the following morning to resume deliberations. On April 11, 2006, the jury deliberated from 9:00 a.m. until 12:00 p.m., and from 1:15 p.m. until 2:30 p.m. At that time, the jury sent a second message to the court, stating that it had reached a decision on three of the questions put to it, but was undecided *440 as to the remaining two. The message further reported that "[w]e have examined the evidence extensively & honestly seem to be at an impasse. What should be done?" In response, the court gave the jury the Sixth Circuit pattern Allen charge over the defendants' objections.
The jury adjourned at 5:30 p.m. and returned at 9:00 a.m. on April 12, 2006. At 10:35 a.m., the jury returned a verdict. Caselaw from this circuit supports the giving of the Allen charge "as soon as the jury announce[s] its deadlock." Tines, 70 F.3d at 896; see also United States v. Sawyers, 902 F.2d 1217, 1220 (6th Cir. 1990) (holding that the district court was within its discretion to give the Allen charge when the jury announced a deadlock after deliberating for three hours). This court has in fact "determined that the possibility of coercion is reduced if the charge is given early rather than after days of deadlocked deliberations." Tines, 70 F.3d at 896. We therefore conclude that the district court did not err in giving the Allen charge.

D. Evidentiary objection and judicial bias
Roach and Sheldon next assert that the district court erred in limiting Roach's cross-examination of Michael Gray, one of the government's witnesses, and that the district court improperly asked questions of two government witnessesChief of Police Maurice Shults and Newport Police Lieutenant Ronnie Landers. These are two different, though related, claims. The first challenges an evidentiary ruling and the second alleges judicial bias against the defendants.

1. Evidentiary objection
The defendants contend that the district court erred when it limited the range of their cross-examination of Michael Gray, a key prosecution witness. Gray testified that he had been on duty as an emergency medical technician at the time of the alleged traffic stop. Specifically, he had been outside his employer's building, washing his personal vehicle, when he observed the traffic stop occur directly across the street. During cross-examination, counsel for Roach elicited testimony that Roach worked part-time for a rival ambulance service and that the ambulance company for which Gray worked had in fact sued Roach's employer. Gray testified that he was aware of the lawsuit but did not know when the complaint was filed. Roach's counsel then attempted to introduce a copy of the civil complaint in that lawsuit to show when it was filed. The court sustained the government's objection that the document was irrelevant.
On appeal, the defendants argue that the copy of the complaint in the lawsuit between the two ambulance services clearly showed that Gray was biased against the defendants and had a reason to lie about seeing them conduct the alleged traffic stop. The government characterizes this as a strained argument. We agree.
A district court's ruling on the admissibility of evidence is reviewed under the abuse-of-discretion standard. United States v. Mack, 258 F.3d 548, 553 n. 1 (6th Cir.2001). The record in the present case reflects that the court gave careful consideration to the excluded evidence, questioned defense counsel about its relevance, and ruled that, in light of Gray's testimony that he did not know when the lawsuit was filed, the actual date of filing stamped on the complaint involving the two ambulance services was irrelevant. On such a record, we conclude that the district court did not abuse its discretion in excluding the document.


*441 2. Judicial bias

Roach and Sheldon further assert that the district court "improperly joined the adversarial proceeding" when it questioned government witnesses regarding matters relating to the defense's theory that the alleged traffic stop never occurred or that, if it did, Roach and Sheldon were not involved. They contend that the district court's questions suggested to the jury that the court did not believe the defense's argument that a different officer, John Jones, was the one who conducted the alleged traffic stop. These questions, according to the defendants, "deprived the proceedings of the appearance of impartiality and thereby destroyed the defendants' chance for a fair trial." United States v. Owens, 159 F.3d 221, 227 (6th Cir.1998).
When a defendant timely objects to the district court's allegedly biased conduct, we apply the harmless-error standard of review. Id. at 227. The plain-error standard of review applies, however, to claims of judicial bias that were not properly preserved by objections in the lower court. Id. In the present case, the defendants preserved their claim regarding the district court's questioning of Chief Shults by objecting to the questioning in a sidebar conference during the next recess in the trial. Their claim of bias arising from the district court's questioning of Lieutenant Landers, however, was not preserved because the defendants failed to object either contemporaneously or at the next available opportunity when the jury was not present. See Fed.R.Evid. 614(c) ("Objections to the calling of witnesses by the court or to interrogation by it may be made at the time or at the next available opportunity when the jury is not present.").

a. Chief Shults
Sheldon's counsel cross-examined Chief Shults about the police department's shift-log for the day of the alleged stop. After the parties had finished questioning Shults, the district court asked several additional questions relating to the shift-log and what information it gave about the work assignment of Jones on that day. The questions established that Jones had been working from 1:00 p.m. until 9:00 p.m. and had been assigned, without a partner, to a patrol car with a light-bar on its roof, not to a slick-top car. When the court concluded, counsel for both defendants then asked additional questions about police practices for reporting a traffic stop or for permitting law enforcement officers from other departments to ride in police cars with on-duty police officers. Neither defendant objected contemporaneously to the court's questioning of Shults. At the next recess in the proceedings, however, counsel for Roach raised an objection to the court's questioning. The following exchange occurred:
MS. PIERCE: Although we did not contemporaneously object to the questioning of Officer Shults by the court, I feel like we need to preserve the record that, you know, perhaps that may have put, you know, some weight on that, you know; and, obviously, I preserve it solely for the record.
THE COURT: So that the record will reflect it totally, the reason I asked the question is Mr. Hill through his questioning suggested to this court and to this jury that another officer was in fact responsible for these crimes. If that's true, if Mr. Hill has any basis for that, he needs to give that information to the FBI.
MS. PIERCE: Very well. Thank you, Your Honor.
THE COURT: And it was left unclear.
We conclude that the district court did not abuse its discretion in questioning *442 Chief Shults. The court asked less than ten questions relating to the hours that Jones worked on the day of the incident, what car he drove, whether he was assigned to the car alone or with a partner, and whether the car had a light-bar on its roof or was a slick-top. A judge trying a criminal case is responsible for ensuring "that the issues are not obscured and that the testimony is not misunderstood." United States v. Hickman, 592 F.2d 931, 936 (6th Cir.1979) (reversing a conviction where the trial court's questions displayed bias against the defendant that violated the latter's right to a fair trial). The court may "interject itself into the proceedings when `necessary to clear up confusion in the evidence or to supplement, in an impartial fashion, the presentation of a poorly prepared attorney.'" McMillan v. Castro, 405 F.3d 405, 410 (6th Cir.2005).
When evaluating a claim of judicial bias, we examine three factors. Hickman, 592 F.2d at 933. The first factor looks at "the nature of the issues at trial," including the length or complexity of the proceedings, and asks whether the judge's intervention was needed "to clarify what is going on." Id. Second, we examine the conduct of counsel for lack of preparation or obstreperousness, and whether "the facts are becoming muddled," because in such cases the court "performs an important duty by interposing clarificatory comments or questions." Id. The third factor evaluates the conduct of the witnesses, recognizing that their "inadvertent" confusion may be resolved by judicial intervention. Id. In the present case, none of these factors support the defendants' argument that the district court's conduct "rendered a fair verdict impossible." Id. at 932.
The district court's questions were brief and direct. They revealed no bias for or against either party. The court expressed no opinion about the witness's responses. To be sure, the district court's explanation of why it asked the questions is puzzling. Its report-to-the-FBI rationale, however, is insufficient to constitute a violation of the defendants' right to a fair trial. The record in the present case reveals that counsel for Sheldon asked Chief Shults several questions designed to elicit information that Jones was on duty at the time of the alleged incident and in fact conducted a traffic stop near the fire station, a building that resembles the Allied EMS station house, at approximately the time of the incident at issue. But the record also indicates that Chief Shults gave conflicting answers to counsel's questions about the colors and markings of the cars used by the Newport Police Department and the Cocke County Sheriff's Department. The court, therefore, was reasonably concerned that the jury would be confused. Under these circumstances, we conclude that the court acted appropriately in questioning the witness to clarify a portion of his testimony.

b. Lieutenant Landers
Roach and Sheldon also allege that the district court erred in questioning Lieutenant Landers at trial. But they fail to develop any arguments in support of this claim in their brief, so we deem the issue to be waived. See United States v. Layne, 192 F.3d 556, 566 (6th Cir.1999) ("[I]ssues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived."). Moreover, even if the defendants had properly preserved the issue, their claim lacks merit. The trial court asked two questions of Landers during the cross-examination by Roach's counsel. These questions were clearly designed to clarify Landers's vague and equivocal response to questions about the make and model of *443 police patrol cars and how many had light-bars on their roofs. Such questioning by the court fulfilled the court's role of clarifying testimony and addressing the apparent confusion of the witness. See United States v. Seago, 930 F.2d 482, 492 (6th Cir.1991) (holding that a comment made by the district court that it agreed with the reasoning of the government's objection to a question by the defense in cross-examination served to "properly clarif[y] the legal context in which the witness'[s] testimony should be considered" and was not biased).

E. Cumulative error
Roach and Sheldon next contend that the cumulative effect of all of the alleged errors that they raise on appeal deprived them, jointly and severally, of their right to a fair trial. This claim appears in Roach's brief in a two-sentence paragraph that is a near-paradigmatic example of perfunctory argument. For this reason, we deem the claim to be waived. Layne, 192 F.3d at 566. In any event, the claim would fail even if it had been more fully developed. Roach and Sheldon have been unable to demonstrate that the district court committed any error in the trial, much less that the cumulative effect of any such errors rendered the trial "fundamentally unfair." See United States v. Blackwell, 459 F.3d 739, 770 (6th Cir.2006) (holding that the "cumulative prejudice of trial errors did not render Defendant's trial fundamentally unfair"). We therefore conclude that the district court did not commit errors that cumulatively resulted in a denial of the defendants' right to a fair trial.

F. Denial of Sheldon's motion to dismiss the superseding indictment
Sheldon separately argues that the district court erred in denying his motion to dismiss the superseding indictment, which contained the additional charge against him of being an accessory after the fact. This added charge was the result, according to Sheldon, of prosecutorial vindictiveness by an Assistant United States Attorney who "let his own agenda trump that of `justice.'" In the original indictment, Sheldon was charged with depriving Gomez and Mejia of their civil rights under color of law and with conspiring to do so. The superseding indictment omitted the conspiracy charge but added a count charging Sheldon alone with being an accessory after the fact.
Due process "prohibits an individual from being punished for exercising a protected statutory or constitutional right." United States v. Poole, 407 F.3d 767, 774 (6th Cir.2005) (citing United States v. Goodwin, 457 U.S. 368, 372, 102 S.Ct. 2485, 73 L.Ed.2d 74 (1982)). But "the Due Process Clause is not offended by all possibilities of increased punishment. . ., [] only by those that pose a realistic likelihood of vindictiveness." Blackledge v. Perry, 417 U.S. 21, 27, 94 S.Ct. 2098, 40 L.Ed.2d 628 (1974) (quotation marks omitted). A defendant alleging prosecutorial vindictiveness must show either "actual vindictiveness" or a "realistic likelihood of vindictiveness." United States v. Dupree, 323 F.3d 480, 489 (6th Cir.2003). Actual vindictiveness is demonstrated by "objective evidence that a prosecutor acted in order to punish the defendant for standing on his legal rights." Id. The realistic-likelihood-of-vindictiveness standard examines the prosecutor's "stake in deterring the exercise of a protected right and the unreasonableness of his actions." Poole, 407 F.3d at 774 (quotation marks omitted).
This court's decision in Poole addresses a situation very similar to the one before us. Poole was indicted on one count of being a felon in possession of a firearm. *444 The district court declared a mistrial because the jury could not reach a unanimous verdict. Id. at 769. Thereafter, the government requested the grand jury to return a superseding indictment that charged Poole with being a felon in possession of a firearm, with possession of a firearm during the commission of a drug crime, and with possession of crack cocaine with the intent to distribute. The grand jury did so. Poole then proceeded to a second trial, where he was found guilty of all three offenses. Id.
On appeal, Poole argued that the district court erred in denying his motion to dismiss the superseding indictment, which he alleged was the result of vindictive prosecution. This court noted that the Supreme Court had not yet addressed a prosecutorial-vindictiveness claim "aris[ing] out of a superseding indictment sought after an initial mistrial." Id. at 774. The court then considered other, related Supreme Court decisions for guidance in analyzing whether there was a realistic likelihood of vindictiveness. Id. at 775.
First, the Poole court noted that "while the timing [of the superseding indictment] certainly does not compel the conclusion that a change in the indictment was a product of vindictiveness, it does make the possibility more likely than would a change at a pretrial stage." Id. at 776. The court also noted that the prosecution's "stake" increases when it is forced to "do over what it thought it had already done correctly." Id. (quoting Goodwin, 457 U.S. at 383, 102 S.Ct. 2485). But the court found persuasive the fact that the government had not objected to the mistrial. Id. at 377, 102 S.Ct. 2485. "Thus, it seems not only that the prosecution welcomed the new trial, it also realized that there was a better way to conduct it." Id. Accordingly, "the government's response to the mistrialseeking a superseding indictmentwas reasonable under the circumstances presented here." Id. The court then concluded that even if Poole had raised a presumption of vindictive prosecution, the government had rebutted any such presumption because "there exist[ed] objective information in the record to justify the increased sentence or additional charges." Id.
In the present case, the superseding indictment added a lesser charge against Sheldon for being an accessory after the fact. Sheldon contends that the government failed to show that the additional charge was based on new evidence or that the charge could not have been brought earlier. See United States v. Suarez, 263 F.3d 468, 480 (6th Cir.2001) ("Generally, a potentially vindictive superseding indictment must add additional charges or substitute more severe charges based on the same conduct charged less heavily in the first indictment. . . . If the prosecution can show that the additional charges were not brought earlier because they were based on new evidence, it will successfully rebut a showing of vindictiveness." (citations omitted)).
Sheldon asserts that because the superseding indictment added a new charge and the government failed to assert that there was any new evidence supporting that charge, the superseding indictment was the result of vindictive prosecution. He contends that the additional charge was added because he had refused to cooperate with the prosecution and to testify against Roach. Sheldon further argues that the government's actions were "reprehensible, unrelenting and justice demands that the verdict rendered be reversed and the remaining charge dismissed." The district court considered virtually identical arguments when it denied the defendants' joint motion to dismiss. Its analysis of *445 Sheldon's claim provides in relevant part as follows:
Based upon the testimony at trial that there was a "good cop" identified as Sheldon and a "bad cop," and based upon the defendants' acquittal on the conspiracy count, it is reasonable to conclude that the jury may have believed that Sheldon was not involved in the actual commission of the crimes alleged in the indictment. However, there was objective evidence that Sheldon's statement after the crimes were committed was consistent with that of Roach and that he was an accessory after the fact attempting to prevent Roach's apprehension and conviction.
Sheldon argues on appeal that the government informed him during the initial investigation that he could be charged with being an accessory after the fact. According to Sheldon, this indicates that the government already had evidence that it thought would support such a charge and thus made a decision not to seek an indictment for that offense in the initial indictment. Sheldon implies, however, that the government sought the accessory charge after the mistrial to punish Sheldon for exercising his constitutional right to a trial. The government responds that the decision to seek the superseding indictment was, as in Poole, based on "a reasoned re-evaluation of the evidence and the existing charges."
To be sure, the government's assertion that it sought a superseding indictment based on a "reasoned re-evaluation of the evidence" after the district court declared a mistrial is rather conclusory. But this lack of elaboration does not by itself establish that the superseding indictment was motivated by prosecutorial vindictiveness. The new charge, for one thing, was a less severe charge than those contained in the original indictment and, for another, was approved by a grand jury and therefore "presumed to have rested on probable cause." Suarez, 263 F.3d at 481. Sheldon does not allege that the "grand jury was manipulated or otherwise prejudiced against him." Id.
Finally, as the district court noted, there was objective evidence in the record that supported the new charge. Sheldon had given a statement to the TBI agent investigating the alleged traffic stop in which he denied making the stop in question or stopping any Hispanic individuals on the day of the incident. When subsequently offered the opportunity to alter or amend that statement, he declined to do so. Accordingly, we conclude that the district court did not err in denying Sheldon's motion to dismiss the superseding indictment.

G. Motion for a new trial
Sheldon also argues that the district court erred when it denied the defendants' joint motion for a new trial. Specifically, Sheldon disagrees with the district court's conclusion that the defendants had "invited" the government's comments about the cell phone and the Ten Commandments.
"The decision to grant or deny a motion for a new trial is entirely within the discretion of the district court, and we will not reverse absent a showing of an abuse of discretion." United States v. Anderson, 76 F.3d 685, 692 (6th Cir.1996). Sheldon contends that the district court improperly considered the arguments of counsel for Roach in denying the motion for a new trial as to Sheldon. To be sure, the court quoted from the closing argument by counsel for Roach, providing no corresponding citation to argument by counsel for Sheldon. But our review of the record reveals that Sheldon's counsel did in fact refer to the cell phone during his closing arguments. In an attempt to raise doubt about *446 the veracity of Gomez's and Mejia's testimony relating to the cell phone, Sheldon's counsel stated in pertinent part as follows:
Agent King had never heard of the cell phone being thrown or anything until recently. . . . And one of the important things that you need to think about when you consider this cell phone, and it's the reason I brought it up, Sandra Bowles [sic], who is a friend of Mr. Mijia's [sic], told you that Mr. Mijia told her that he had called his wife on the cell phone right after it happened. Check the records, it's not there. It's not there.
These comments may not have been as direct an invitation as those made by counsel for Roach, but they support the district court's denial of the motion for a new trial.
As to the government's reference to the Ten Commandments, we note that Sheldon's counsel did not contemporaneously object. Moreover, for the reasons previously discussed in Part II.A.1.b. above, the government's comments, although improper, were not flagrant and did not appeal to religious or ethnic prejudice. We therefore conclude that the district court did not err in denying the motion for a new trial as to Sheldon.

H. Sufficiency of the evidence
Finally, both Roach and Sheldon assert that the government failed to produce sufficient evidence to support their convictions. As with their claim regarding cumulative error, the defendants present a perfunctory and conclusory treatment of this claim. Roach justifies this deficiency because of "the word limit on appellate briefs which limits a full development of the issue in favor of issues on appeal also deserving of relief." But neither Roach nor Sheldon sought leave to exceed the word limit. Their lack of argumentation alone condemns their sufficiency-of-the-evidence claim. See United States v. Layne, 192 F.3d 556, 566 (6th Cir.1999).
Even assuming that the claim was properly presented, moreover, the defendants cannot carry their "heavy burden." See United States v. Jefferson, 149 F.3d 444, 445 (6th Cir.1998). The standard of review for Roach's and Sheldon's challenge to the sufficiency of the evidence against them is "whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." United States v. Davis, 473 F.3d 680, 681 (6th Cir.2007) (quoting Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (emphasis in original)).
Gomez and Mejia each testified that the minivan in which they were traveling was stopped by Roach and Sheldon, and that Roach took money from Mejia's wallet. Gray corroborated their testimony about the stop. Video surveillance photos taken at Wal-Mart contradicted the defendants' alibis. Testimony from Lieutenant Landers and from TBI Agent King established that Sheldon denied that the stop occurred, and that he repeated his statement when subsequently presented with the opportunity to add to or amend it. All told, this evidence is sufficient to support the jury's verdict.

III. CONCLUSION
For all of the reasons set forth above, we AFFIRM the judgment of the district court on all grounds. We also AFFIRM the denial of Roach's bond pending appeal because he failed to raise a substantial question of fact or law that would overcome the presumption against release on bond after conviction. See United States *447 v. Chilingirian, 280 F.3d 704, 709 (6th Cir.2002).
NOTES
[*]  The Honorable Harold A. Ackerman, Senior United States District Judge for the District of New Jersey, sitting by designation.
