
609 F.3d 663 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Len DAVIS, Defendant-Appellant.
No. 05-31111.
United States Court of Appeals, Fifth Circuit.
June 16, 2010.
*670 April J. Anderson, Gregory Bryan Friel (argued), Dept. of Justice, Civ. Rights Div., Appellate Section, Washington, DC, Michael Edward McMahon, Stephen Andrew Higginson, Asst. U.S. Attys., New Orleans, LA, for Plaintiff-Appellee.
Barry Joseph Fisher (argued), Albany, NY, Marcia Adele Widder (argued), New Orleans, LA, for Defendant-Appellant.
Before STEWART, DENNIS and HAYNES, Circuit Judges.
CARL E. STEWART, Circuit Judge:
Defendant-appellant Len Davis appeals his 1996 conviction and 2005 death sentence imposed pursuant to the Federal Death Penalty Act ("FDPA"), 18 U.S.C. §§ 3591-3599. We AFFIRM.

I.

A.
Kim Marie Groves was murdered on October 13, 1994 in New Orleans, Louisiana, through the coordinated efforts of Davis and his co-conspirators Paul Hardy and Damon Causey. Davis, then an officer with the New Orleans Police Department ("NOPD"), exchanged protection for favors with Hardy, then a New Orleans drug dealer. Causey was an associate of both Hardy and Davis. One of Hardy's favors, at Davis's request, was to murder Groves.
Davis requested the murder because, on or about October 10, 1994, Groves witnessed Davis's police partner, Sammie Williams, pistol-whip her "nephew," Nathan Norwood, who lived in the neighborhood. Groves filed a complaint against Davis with the NOPD's internal affairs office, alleging that Davis engaged in police brutality.
Davis learned about the complaint on October 12. The next day, Davis paged Hardy at about 5 p.m. When Hardy called back, he and Davis discussed a plan to kill Groves, with Hardy as the shooter and Davis and Williams taking care of evidence at the crime scene after the murder was committed. Davis arranged to meet Hardy and Causey at the police station to view photos of homicide cases. Davis and Williams then drove to Groves's neighborhood in their NOPD patrol car and searched for her. Shortly after 7:30 p.m., Davis and Williams picked up Hardy at his home and drove back to Groves's neighborhood so that Hardy could walk around.
After driving Hardy home, Davis and Williams returned to Groves's neighborhood and searched for her again. Davis became agitated as the evening progressed because Groves had not been killed yet. At about 9:45 p.m., Davis called Hardy to complain; Hardy assured him that the murder would get done.
At approximately 10:00 p.m., Davis and Williams spotted Groves near her home. Davis paged Hardy. When Hardy called Davis back almost immediately, Davis described Groves's appearance. Hardy replied he was "on [his] way." Williams's shift ended at that point, and he left Davis with the patrol car.
*671 About 45 minutes later, Davis called Hardy again to complain that Hardy had not killed Groves yet, and described Groves's clothing and location in detail. Hardy, along with Causey and a driver, went to Groves's neighborhood. At approximately 11:00 p.m., Hardy shot Groves in the head, killing her.
At the time he was planning the murder with Hardy and Causey, Davis was unaware that he was the target of an FBI undercover investigation into corruption in the NOPD. That investigation, "Operation Shattered Shield," involved soliciting NOPD officers to guard what they thought was a warehouse holding illegal drugs for shipment. In connection with this investigation, the FBI conducted surveillance and recorded cellular telephone conversations of Davis and other NOPD officers.

B.

1.
In December 1994, the Government filed a one-count federal indictment against Davis, Hardy, and Causey, followed by a three-count superseding indictment and a second superseding indictment. In July 1995, pursuant to the FDPA, the Government filed two notices of intent to seek the death penalty for Davis and Hardy, and the FDPA elements in support. See 18 U.S.C. § 3593(a).
In August 1995, the third superseding indictment charged each defendant with: (1) conspiracy to deprive Groves of her civil rights while acting under color of state law, including eight overt acts in furtherance of the conspiracy, in violation of 18 U.S.C. § 241; (2) depriving Groves of her civil rights by use of excessive force by shooting her with a firearm, resulting in death, in violation of 18 U.S.C. §§ 242 and 2; and (3) willfully killing Groves to prevent her communications to a law enforcement officer regarding a possible federal crime, in violation of 18 U.S.C. §§ 1512(a)(1)(C) and 2.
In April 1996, Davis and his co-defendants were tried jointly before a jury. The evidence included recorded telephone conversations between Davis and Hardy discussing Groves's complaint and the plan to shoot her. Williams also testified and corroborated much of the recorded conversations. The jury found Davis and Hardy guilty on all three counts, and found Causey guilty on Counts 1 and 2; it could not reach a verdict on Count 3 as to Causey. After the conviction, Davis refused to return to the courtroom and the case proceeded to the sentencing phase in his absence.
At the first stage of the sentencing phase, the jury was charged to decide whether an FDPA "death qualifying factor" existed for either Davis or Hardy. See 18 U.S.C. §§ 3592, 3593(d). The jury found that Davis and Hardy intentionally killed Groves after substantial planning and premeditation. Accordingly, the district court conducted a hearing at the second stage of the sentencing phase to determine whether Davis and Hardy should be sentenced to death or to life imprisonment without release. See id. § 3592. The jury selected the death penalty. Davis and Hardy were sentenced to death; Causey, to life imprisonment.

2.
All three defendants appealed, citing numerous points of error individually and collectively. We affirmed Causey's conviction and sentence, and affirmed Davis's and Hardy's convictions on Counts 1 and 2. United States v. Causey, 185 F.3d 407, 412-21 (5th Cir.1999), cert. denied, 530 U.S. 1277, 120 S.Ct. 2747, 147 L.Ed.2d 1010 (2000). However, we reversed Davis's and Hardy's convictions on Count *672 3 because of insufficient evidence. Id. at 421-23. We also vacated Davis's and Hardy's death sentences as to all three counts because the jury did not make separate recommendations concerning the appropriate penalty for each count of the conviction. Id. at 423. Accordingly, we remanded Davis's and Hardy's cases for re-sentencing. Id.

3.
On remand, the Government again sought the death penalty, notifying Davis and Hardy of the FDPA elements in support. Hardy and Davis moved to prohibit a death penalty re-sentencing based on double jeopardy. The district court denied the motion, refusing "to extrapolate from the Fifth Circuit's decision [in Causey] a determination that the Government did not prove its case for death with regard to Counts 1 and 2 because the evidence had been insufficient to sustain a conviction on Count 3." We affirmed the ruling. United States v. Hardy, 34 Fed.Appx. 962 (5th Cir.2002) (per curiam).
Davis moved for reconsideration, arguing that the death sentences were precluded by the indictment's failure to include the requisite specific intent element and statutory aggravating factor under the FDPA. The district court granted Davis's motion in part in an unpublished order, holding that the indictment was insufficient. The Government appealed. We vacated the district court's order, holding that failure to include the required elements was harmless constitutional error, and remanded for re-sentencing. United States v. Davis, 380 F.3d 821, 829-30 (5th Cir.2004), reh'g & reh'g en banc denied, 121 Fed.Appx. 59 (5th Cir.2004) (table), cert. denied, 544 U.S. 1034, 125 S.Ct. 2247, 161 L.Ed.2d 1062 (2005).

4.
Davis's re-sentencing proceedings began on July 25, 2005 before a jury.[1] During the first stage of the re-sentencing, Davis elected to represent himself with appointed counsel serving as back-up.[2] On August 3, 2005, the jury returned a verdict rendering Davis eligible for the death penalty, finding that he intentionally participated in an act contemplating that Groves would be killed, and did so after substantial planning and premeditation. Thereafter, Davis refused to return to the courtroom for the second stage of the re-sentencing, but permitted his back-up counsel to proceed in his absence. After hearing the Government's and defense counsel's evidence, the jury returned a verdict recommending the death penalty, finding that the aggravating factors were proved beyond a reasonable doubt, that no mitigating factors were present, and that the aggravating factors sufficiently outweighed the mitigating factors to justify a death sentence.
On August 17, 2005, Davis filed a motion for judgment of acquittal and a new trial. The district court denied the motion on October 20, 2005, because the issues presented had been decided in numerous motions before Davis's re-sentencing. The *673 district court sentenced Davis to death on October 27, 2005. Davis timely appealed.

II.
Upon conviction for a homicide, the FDPA provides for a separate, post-conviction penalty proceeding. 18 U.S.C. § 3593(b); see also Jones v. United States, 527 U.S. 373, 407-08, 119 S.Ct. 2090, 144 L.Ed.2d 370 (1999).
In the first, or "eligibility" phase of the proceeding, a jury must unanimously find beyond a reasonable doubt that: (1) the victim's death resulted from the defendant's intentional engagement in life-threatening activity; and (2) one or more of the aggravating factors proposed by the Government is present. See 18 U.S.C. §§ 3591(a)(2), 3592(c); Jones, 527 U.S. at 407-08, 119 S.Ct. 2090.
If the jury returns both findings, the proceeding moves to the second or "selection" phase. See 18 U.S.C. § 3593(e). Here, the jury decides whether the aggravating factors sufficiently outweigh statutory or non-statutory mitigating factors to warrant a death sentence or, absent mitigating factors, whether the aggravators alone warrant that sentence. Id.; see also id. § 3592(a); Jones, 527 U.S. at 408, 119 S.Ct. 2090. "The weighing is not numeric; the perceived significance, not the number, of aggravating and mitigating factors determines the decision." Jones, 527 U.S. at 408, 119 S.Ct. 2090. While the jury determines aggravating factors unanimously and beyond a reasonable doubt, it determines mitigating factors individually and by "a preponderance of the information." 18 U.S.C. § 3593(c), (d). In other words, "a mitigating factor may be considered in the jury's weighing process if any one juror finds the factor proved by a preponderance." Jones, 527 U.S. at 408, 119 S.Ct. 2090.
Based on its consideration of the aggravating and mitigating factors, the jury decides unanimously whether the defendant shall be sentenced to death, to life imprisonment without possibility of release, or some other lesser sentence. 18 U.S.C. § 3593(e).
The FDPA further prescribes our review of a death sentence imposed pursuant to its procedures. We may not reverse or vacate a sentence of death "on account of any error which can be harmless, including any erroneous special finding of an aggravating factor, where the Government establishes beyond a reasonable doubt that the error was harmless." Id. § 3595(c)(2).

III.
Davis alleges eight points of error in the re-sentencing hearings. We examine his claims in turn.

A.
In his first claim, Davis challenges the sufficiency of the evidence to support the sentencing jury's finding that he posed a threat of future dangerousness while imprisoned.
During the second or selection phase of Davis's re-sentencing hearing, the Government presented evidence to prove that Davis posed a threat of future dangerousness while imprisoned, a non-statutory aggravating factor. See 18 U.S.C. § 3592(b) ("The jury ... may consider whether any other aggravating factor for which notice has been given exists."). First, the Government resubmitted the evidence presented in the first or eligibility phase that proved Davis acted with specific intent and after substantial planning and meditation, resulting in Groves's death. The testimony and wiretap excerpts from Operation Shattered Shield revealed that Davis's sole motivation for ordering Groves killed was *674 the complaint she filed against him. Second, the Government presented evidence of Davis's history of using sophisticated methods to conduct criminal activity. The evidence showed that, besides orchestrating Groves's murder, Davis routinely used special codes to communicate with Hardy and Causey, and offered to assist them in covering up their criminal activities. Third, the Government presented video surveillance from Operation Shattered Shield. Special Agent Juan Jackson, the undercover FBI agent acting as a drug dealer, testified that Davis was a leader in what he thought was a major drug operation and increased his responsibilities in the operation in a few months' time span. Williams, Davis's partner in 1994, also testified that Davis recruited other police officers to guard warehouses of drugs and to escort drug couriers in their deliveries, and that Davis paid the recruits from money received from the undercover FBI agent. Finally, the Government presented instances during Davis's incarceration in which he talked back to prison guards and was involved in disciplinary infractions.
During the mitigation case at the selection phase, defense counsel presented Davis's incarceration records for the previous eleven years (from his arrest in 1994 to his 2005 re-sentencing). The records showed that Davis had two minor disciplinary incidents for most of his incarceration (possession of an unauthorized newspaper and failure to submit to DNA testing).
At the close of the selection phase hearing, the district court charged the following aggravating factor to the jury: "That Mr. Davis poses a threat of future dangerousness to the lives and safety of other persons while imprisoned." The jury unanimously found that the Government had proven this factor beyond a reasonable doubt.
The FDPA requires this court to review whether the evidence supports a special finding of the existence of an aggravating factor. 18 U.S.C. § 3595(c). Accordingly, "[this court] reviews jury findings of aggravating factors by asking whether, after viewing the evidence in a light most favorable to the government, any rational trier of fact could have found the existence of the aggravating circumstance beyond a reasonable doubt." United States v. Agofsky, 458 F.3d 369, 374 (5th Cir.2006) (citing United States v. Bernard, 299 F.3d 467, 481 (5th Cir.2002)).
We have defined future dangerousness as evidence that a defendant is "likely to commit criminal acts of violence in the future that would be a threat to the lives and safety of others." Bernard, 299 F.3d at 482. In June 2005, the district court granted that part of Davis's motion which limited this factor to his threat of future dangerousness while he is in a penal institution.
Davis asserts that the Government's evidence amounts to no more than him placing phone calls to protect Hardy's violent crimes or to recruit others in a drug conspiracy and not to actual acts of violence. "But advancing a different assessment of the evidence or urging conflicting inferences therefrom does not demonstrate a legal inadequacy in the government's proof." United States v. Fields, 516 F.3d 923, 943 (10th Cir.2008). Instead, we consider the evidence in a light most favorable to the Government. Id.; see also Agofsky, 458 F.3d at 374. Here, the Government's evidence supported the theory that Davis's modus operandi was to direct other persons to commit criminal acts and to inflict violence on other persons. Our review of the record reflects that in Davis's interactions with associates like Hardy, Causey, and others, Davis gave directions, offered advice, and assisted *675 in his associates' nefarious activities.[3] His leadership role and ability to influence othersgenerally positive qualitiesbecame deadly when exercised to further criminal activity. Such a pattern of behavior could easily translate to a penitentiary. See Bernard, 299 F.3d at 482 (concluding that evidence of propensity for orchestrated criminal activity in prison permitted finding of future dangerousness).
Davis also places much weight on evidence of his violence-free prison record during the 11 years between his arrest in 1994 and his sentencing in 2005. He is correct that "evidence suggesting that he had been a well-behaved and disciplined prisoner" is "highly relevant" to the jury's sentencing determination. See Skipper v. South Carolina, 476 U.S. 1, 7 n. 2, 106 S.Ct. 1669, 90 L.Ed.2d 1 (1986). On these facts, however, length of incarceration without violence is not dispositive to the issue of whether Davis is a threat of future dangerousness while imprisoned. Stated another way, evidence of Davis's past dangerousness is not negated by non-violent conduct in prison during a time when he is "on display" while the appeal of his death sentence is pending.
Viewing the evidence in a light most favorable to the Government, see Agofsky, 458 F.3d at 374, the jury could have found the future dangerousness factor beyond a reasonable doubt. Therefore, we affirm the jury's finding on the future dangerousness factor.

B.
In his second claim, Davis argues that the district court committed reversible error when it provided an ex parte response to a jury question during deliberations.
At the close of the selection phase, the district court invited objections from counsel regarding the jury instructions. Defense counsel offered correction to a typo but no substantive objections. The court then charged the jury that they must decide whether Davis posed "a threat of future dangerousness to the lives and safety of other persons while imprisoned." (emphasis added). The special interrogatory on the verdict forms, however, asked whether he posed "a threat of future dangerousness to the lives and safety of other persons in prison." (emphasis added).
During deliberations, the jury sent the following note to the judge:
Please clarify which is correct. Count OnePart B states: "... in prison." On Pg 9Issues to be decided states: "... while imprisoned."
The district court judge responded in writing: "I apologize for the different terminology. It's intended to mean the same thing."
The parties contest whether the district court judge notified trial counsel before responding to the jury's question. Davis contends that the judge responded without receiving input from counsel. The Government asserts that the lead prosecutors do not recall whether the district court discussed the note with the parties. However, the Government agrees that the judge erred if, in fact, she answered the jury's question without first consulting counsel for both parties.
*676 It is well-settled in this circuit that when a communication is received from the jury, counsel should be informed of its substance and afforded an opportunity to be heard before a supplemental charge is given. United States v. Bieganowski, 313 F.3d 264, 293 (5th Cir.2002) (citing United States v. McDuffie, 542 F.2d 236, 241 (5th Cir.1976)); United States v. Sylvester, 143 F.3d 923, 928 (5th Cir. 1998) ("Upon receiving the note from the jury, the court should have notified counsel of the message, shared its contents and granted each side the opportunity to be heard."). Our review of the record comports with Davis's contention, because there is no evidence that the district court judge notified the parties before answering the jury's question. Without the notification, Davis and his counsel were unable to "evaluate the propriety or adequacy of the proposed supplemental charge, formulate objections, or suggest additional instructions." McDuffie, 542 F.2d at 241. Therefore, we hold as a matter of law that the district court committed error when it failed to notify the parties before responding to the jury.
However, "[w]e recognize that an error of this kind may, depending on the facts and circumstances of the case, be harmless." Id.; see also United States v. Hillsman, 480 F.3d 333, 335-36 (5th Cir. 2007); United States v. Hall, 152 F.3d 381, 406 (5th Cir.1998), abrogated on other grounds by United States v. Martinez-Salazar, 528 U.S. 304, 120 S.Ct. 774, 145 L.Ed.2d 792 (2000). In this context, the error is harmless if the answer is responsive to the question, correctly states the law, and no prejudice results. Sylvester, 143 F.3d at 928. We also determine whether it appears "beyond a reasonable doubt that the error complained of did not contribute to the verdict obtained." Hall, 152 F.3d at 406 (citing Chapman v. California, 386 U.S. 18, 23, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967)); see also 18 U.S.C. § 3595(c)(2).
Davis argues that the response "they were intended to mean the same thing" is non-responsive and incorrect. But the most reasonable reading of the district court's answer is that the jury should have considered Davis's threat of future dangerousness while imprisoned or in prison i.e., that the terms are interchangeable, and the wording discrepancy was a clerical error. The judge's answer is thus consistent with her prior order dated June 27, 2005, which limited the aggravating factor regarding Davis's threat of future danger:
The Court agrees with Defendant's contention, however, that this non-statutory aggravating factor must be qualified to indicate to the jury that it should consider Davis's future dangerousness only within the context of any menace he might present in a penal institution. This qualification is necessary because for the jury the alternative to the death penalty will be an imposition of life imprisonment. See United States v. Cooper, 91 F.Supp.[2d] 90, 111-112 (D.D.C. 2000) ("[W]hatever violent or criminal capabilities Cooer [sic] has outside the prison walls will have no probative value when ... [he] will spend the rest of his life in prison....")
Davis further argues that the jury may have been confused because "while imprisoned" implied the length of time Davis would be incarcerated (and possibly released), while "in prison" denotes the fact that he would be incarcerated (with no release). Without an opportunity to provide input into the correct answer, he argues, the jury was misled.
While we agree that counsel did not have an opportunity to provide input, we disagree that the jury was misled. The jury was awarefrom the court's detailed *677 instructions before and after the selection and penalty phasesthat Davis could only be sentenced to a life sentence without the possibility of release, or to death. The verdict form and the jury instructions plainly said so. We presume that the jury follows their instructions. United States v. Millsaps, 157 F.3d 989, 993 (5th Cir. 1998) (citing Zafiro v. United States, 506 U.S. 534, 540, 113 S.Ct. 933, 122 L.Ed.2d 317 (1993)). Davis thus was not prejudiced by the district court's error.
Under our established precedent, the district court's failure to notify the parties before replying to the jury's question was error. Nonetheless, we hold that the facts and circumstances of this case make the error harmless. McDuffie, 542 F.2d at 241. We therefore will not reverse Davis's sentence on this ground.

C.
In his third claim, Davis alleges that the prosecution engaged in misconduct by (1) introducing evidence about his and Hardy's involvement in violence; (2) improperly cross-examining his defense expert; and (3) presenting arguments to the jury about Davis's and Hardy's involvement in violence, in violation of his due process rights.
Generally, we apply a two-step analysis to claims of prosecutorial misconduct. United States v. Fields, 483 F.3d, 313, 358 (5th Cir.2007), cert. denied, 552 U.S. 1144, 128 S.Ct. 1065, 169 L.Ed.2d 814 (2008). First, we assess whether "the prosecutor made an improper remark." Id. If so, then we ask whether the defendant was prejudiced. Id. The prejudice step "sets a high bar ... The determinative question is whether the prosecutor's remarks cast serious doubt on the correctness of the jury's verdict." Id. (internal citation omitted). We generally look to three factors in deciding whether any misconduct casts serious doubt on the verdict: "(1) the magnitude of the prejudicial effect of the prosecutor's remarks, (2) the efficacy of any cautionary instruction by the judge, and (3) the strength of the evidence supporting the conviction." Id. (citing United States v. Mares, 402 F.3d 511, 515 (5th Cir.), cert. denied, 546 U.S. 828, 126 S.Ct. 43, 163 L.Ed.2d 76 (2005)).
Because there was no contemporaneous objection to the testimony, the line of cross-examination, or the prosecutor's arguments, we review each act of alleged misconduct for plain error. United States v. Jackson, 549 F.3d 963, 974-75 (5th Cir. 2008), cert. denied, ___ U.S. ___, 130 S.Ct. 51, 175 L.Ed.2d 43 (2009); Causey, 185 F.3d at 418. To prove plain error, Davis must "show (1) there was error, (2) the error was plain, (3) the error affected his substantial rights, and (4) the error seriously affected the fairness, integrity or public reputation of judicial proceedings." Jackson, 549 F.3d at 975.[4]

1.
To establish Davis's relationship with Hardy and Hardy's reputation for violent acts, the Government presented testimony from Williams, Davis's partner in 1994 and friend since 1990, and Leon Duncan, Davis's partner before Williams.[5] Davis argues that Williams's and Duncan's testimony *678 regarding Hardy's violence impermissibly suggested that Hardy was a killer and that Davis was somehow involved in the killings.
During the first or eligibility phase of the trial, Williams testified that Davis introduced him to Hardy. When asked by the prosecutor, "What did Paul Hardy do?," Williams replied: "He was known in the Florida project where he resided as a drug dealer and a killer." Davis, who conducted the cross-examination,[6] and his back-up counsel did not object to these statements.
During the second or selection phase, Duncan testified that he was familiar with Hardy because he had handled murder cases in which Hardy was a suspect. Duncan further testified about a conversation that he and Davis had about Hardy during a 1994 cookout at Davis's house:
[PROSECUTOR]: Who got a phone call?
[DUNCAN]: Len Davis got on the phone and he told the individual on the phone, yeah, yeah, I'm home, yeah, it's just me, Dunc and Lemmie [Rodgers, another police officer], yeah, just come on over. When I asked him who was that, because I'm thinking it was policemen that he was inviting over since he was having a cookout, I think he's inviting policemen over. And he said, oh, that's Paul. I said, Paul, Paul Hardy? He said, Yeah. What the fuck are you doing hanging out with a cold-blooded killer like Paul Hardy? And he said, man, Paul Hardy ain't never killed nobody that didn't deserve to die. Who the fuck are you or Paul Hardy to decide who lives or die? And he made the statement, well, Dunc, you just don't understand the game. I said, fuck the game, we talking about people's lives. And he said, you see, that's your problem now.
Davis's back-up counsel did not object to these statements.[7]
Under the FDPA, information is admissible during the sentencing hearing regardless of its admissibility under the Federal Rules of Evidence, but "may be excluded if its probative value is outweighed by the danger of creating unfair prejudice, confusing the issues, or misleading the jury." 18 U.S.C. § 3593(c). "Therefore, the defendant and the government may introduce any relevant information during the sentencing hearing limited by the caveat that such information be relevant, reliable, and its probative value must outweigh the danger of unfair prejudice." United States v. Jones, 132 F.3d 232, 241 (5th Cir.1998). "[T]he relaxed evidentiary standard does not impair the reliability or relevance of information at capital sentencing hearings, but helps to accomplish the individualized sentencing required by the constitution." Id. at 242.
In this case, admitting Williams's and Duncan's testimony regarding Hardy's reputation as a killer was not plain error. In 1999, we rejected a similar argument Davis made in his first appeal when he challenged another witness's testimony regarding Hardy's drug-related violent acts:
Evidence that Davis and Hardy were... involved in illegal activities that included violent crimes and drug dealing was relevant to prove both opportunity and motive under the Government's theory *679 of the case, which was that Hardy was willing to execute Groves and Davis was able to order that execution, because of their mutual involvement in these activities, and because of Davis's status as a police officer.
Causey, 185 F.3d at 419. Here, in the eligibility phase, Williams's testimony was relevant to show that Davis was familiar with Hardy's criminal activities, maintained a relationship with him, and therefore was able to call upon him as an intermediary to execute Groves. In the selection phase, Duncan's testimony was relevant to rebut Davis's mitigation evidence regarding residual doubt as to his innocence. Further, the testimony is reliable because both witnesses testified that they were familiar with Hardy's reputation from their own interactions with him and with Davis. Finally, the testimony's probative value in demonstrating Davis's propensity for violent acts outweighs the danger of prejudice. Jones, 132 F.3d at 241. Admission of the testimony is not sufficient to reverse Davis's sentence.

2.
Davis also challenges the prosecution's cross-examination of Dr. Thomas Streed, a former police officer and now an applied psychologist, during the second or selection phase of the re-sentencing hearing. Streed was the defense's only mitigation witness. Defense counsel offered Streed as an expert in police administration, procedures, training, supervision, and administration "with particular emphasis" on "the description and analysis of stress affecting law enforcement officers, and particularly officer-involved use of force cases."
On direct examination, Streed testified based on his review of Davis's police records from 1988 through his arrest in 1994. Streed described several incidents in which Davis had been assaulted or threatened with violence on the job, and his subsequent behavioral changes including alcohol use and increased internal-affairs complaints brought against him. To establish that Davis had worked in a high-crime area, defense counsel showed Streed two pages of crime statistics, which revealed that the Fifth District, where Davis was assigned after 1989, was a higher crime zone than any other NOPD district and in 1994 had one-third of all the city's homicides. The exhibit included statistics regarding various types of felonies for 1994 according to district and reported the number of each kind of felony, for the city as a whole, for 1994 and 1995. The document also showed the percentage change for the two years.
On cross-examination, the Government questioned Streed regarding his knowledge of Davis's case, the Fifth District, Operation Shattered Shield, and other people involved in the case.
Q. Now, do you believe in coincidences, Dr. Streed?
A. In coincidences?
Q. Yes.
A. Yes, I do.
Q. You examined as well as Mr. Davis' personnel file, crime statistics for New Orleans for the year 1994, did you not?
A. Yes, sir.
Q. Anything significant that you're aware of as to the homicide rate, homicide number in 1994?
A. Well, other than the fact that it is considerably higher than the other eight districts, no.
Q. Actually, it was a record.
A. Well, I haven't seen the, you know, the previous years' crime statistics, *680 so I'll accept that, but I don't know that that's true.
Next, after establishing that Streed was familiar with Causey and Hardy, the prosecutor asked if Streed was aware of a war between Hardy and "Poonie", another drug dealer in the Florida housing project located in the Fifth District, in 1994. Streed replied that he was not. The prosecutor continued with questions about the population and crime statistics in the Florida project:
Q. Dr. Streed, actually do you know which project is the smallest in New Orleans, well, back in 1994 population-wise?
A. I can't recall.
Q. Would it surprise you if I said it was the Florida?
A. It would be irrelevant to me.
Q. Well, back in that record year of homicides back in 1994, the Florida housing project led all other projects with 23 homicides
THE COURT: [Prosecutor], you're testifying.
[PROSECUTOR]: I am asking him if he would be surprised at that.
[PROSECUTOR]. Did you research that, Dr. Streed?
A. No.
THE COURT: [Prosecutor], please try not to testify and give information. I understand what you're trying to say, but please.
[PROSECUTOR]: Back to coincidences now, your Honor.
[PROSECUTOR]: The next year, 1995, the Florida only had four homicides.
THE COURT: [Prosecutor], please stop testifying in your questions. If you have a question, ask him a question. You can use evidence that's admissible and been admitted, but please don't go beyond that.
Q. How much investigating did you do, Dr. Streed, apart from the sheer and the bare numbers of the crime stats of 1994; I mean, did you compare things with '95?
A. No, sir.
Q. Did you ask about the significance of numbers of homicides in the various projects?
A. I am sorry, I don't think I understand your question.
Q. I mean the significance that Paul Hardy and Mr. Poonie had this little war in the Florida project. Did you ever talk to any FBI agent who was investigating street violence for a little bit of background?
A. I wasn't aware that there was a war going on between those two people, so I wouldn't have investigated it.
Defense counsel did not object to any of the prosecutor's questions.
Davis argues that this line of cross-examination implied that he and Hardy were responsible for the crime in the Fifth District. Specifically, Davis believes the prosecutor used his cross-examination of Streed to bring before the jury the unsubstantiated claim that the Florida project had an unusually high number of homicides in 1994 (23 total), and that the number had dropped to only 4 homicides in 1995, "coincidentally" after Hardy and Davis were arrested. The net effect of the prosecutor's "testifying," according to Davis, conveyed to the jury that Hardy and Davis were responsible for the differencei.e., almost 20 homicides in 1994.
A prosecutor is allowed to ask questions in cross examination provided he has "some good-faith factual basis for the incidents inquired about." United States v. Bright, 588 F.2d 504, 512 (5th Cir.1979) (citation omitted), cert. denied, 440 U.S. *681 972, 99 S.Ct. 1537, 59 L.Ed.2d 789 (1979). However, "[t]hat does not mean that the basis in fact must be proved as a fact before a good faith inquiry can be made." United States v. Nixon, 777 F.2d 958, 970 (5th Cir.1985). "[T]he government does not have a duty in every case to introduce the factual predicate for a potentially prejudicial question posed on cross-examination." United States v. Jungles, 903 F.2d 468, 478 (7th Cir.1990). This principle "receives even more play where there is no contemporaneous objection to the cross-examination." Id.
Here, the prosecutor's improper statements do not rise to the level of plain error. The prejudicial effect of the prosecutor's improper "did you know ... ?" questions was tempered significantly when the district court admonished him to refrain from that type of questioning. While the bell could not be unrungi.e., the jury had already heard the prosecutor's "testifying"the judge's sua sponte admonitions to the prosecutor alerted the jury to the improper nature of the remarks even without defense counsel's objections or a curative instruction. Cf. United States v. Wicker, 933 F.2d 284, 290 (5th Cir. 1991) (no plain error where "not only was there no objection, but also the district court interrupted the prosecutor sua-sponte immediately after these comments were made to remind her that she was making an improper argument" and provided a general cautionary instruction to the jury).
Moreover, the general line of questioningthough not the formwas appropriate given the topics introduced in direct examination. Streed testified on direct regarding the effects of violent criminal activity on Davis's mental and physical health. The defense introduced the crime statistics during direct examination to support the theory that Davis was a product of the violent atmosphere in which he worked, thus opening the door to the Government's questions on cross-examination. Additionally, the questions about Hardy's war with Poonie tested Streed's knowledge of the case. There was a good-faith factual basis for the questioning, because Williams had already testified that Poonie was a dealer in the Florida project who was one of Hardy's enemies. Moreover, the jury had already heard wiretap excerpts of Davis and Hardy discussing Hardy's war with Poonie, demonstrating that Davis was aware of Poonie's and Hardy's rivalry. Cf. United States v. Johnston, 127 F.3d 380, 393 (5th Cir.1997) (prejudice mitigated by curative instruction and wiretap evidence to corroborate improperly solicited testimony in cross-examination). Further, the Government did not mention Poonie during any other point in the trial, and did not argue about Poonie or his war with Hardy in summation. Accordingly, the prosecutor's "testifying", while improper, see Berger v. United States, 295 U.S. 78, 84, 55 S.Ct. 629, 79 L.Ed. 1314 (1935), did not affect Davis's substantial rights.

3.
Finally, Davis argues that the Government's remarks in summation suggested that Hardy was a killer. At the eligibility phase, the prosecutor opened by telling jurors they would hear how "Davis had developed a particular relationship with Paul Hardy," a "street assassin to the extent where he protected Hardy." Then, in summation, the prosecutor used similar language to discuss Hardy while playing some of the wiretap tapes:
You know too from the tapes and testimony of Sammie Williams that the defendant is protecting a murder [sic] and dope dealer by the name of Paul Hardy.
... They [Davis and Hardy] are friends. You hear it, they talk about families, girlfriends, they talk about things other *682 than the business of dope and the business of murder.
You recall the events of September 30th, 1994, Williams described to you. Williams see [sic] a homicide and what does he do? He calls Davis. And what does Davis, the defendant, do? ... The very first thing he does is call a murderer and dope dealer called Paul Hardy.
At the selection phase, the prosecutor again argued that Hardy was a killer by trade, and that Davis had aided and abetted Hardy and his associates in their criminal activities. Among other comments, the prosecutor told jurors that Davis "was basically the Godfather on the street to a hit squad." The prosecutor also said: "He was protecting Hardy and Causey who were killing people" and referred to Hardy and Causey as Davis's "murdering, drug-dealing friends." According to the prosecutor, Davis "made sure the coast was clear so Hardy and Causey can go do drive-bys. He preyed on a community, this community, New Orleans, Louisiana... that desperately needed, still needs protection from the likes of Davis." "If anybody kills somebody in the Florida, who is the first one they think of? They think of Paul Hardy." As with the opening statement, the prosecutor interspersed his comments with excerpts from the wiretap tapes.
During rebuttal summation, the prosecution also argued that, "The city of New Orleans had to endure the reign of terror of Len Davis and the murderers he was protecting." According to this argument, the surveillance recordings showed Davis as an "unrepentant, narcissist killer who is willing to unleash people like Paul Hardy on the citizens of New Orleans and anybody who dared, had the audacity to dare to stand up to Len Davis." The prosecutor also stated that Davis was a "police officer who routinely not only protected drug dealers and murderers but also actively counseled them on how and when to commit murder and mayhem." The prosecutor told jurors that Davis deserved no mercy, because he had misused his position as a police officer "not to protect and serve the citizens of the community, but to terrorize them and to victimize them." The prosecutor argued, "You see, ladies and gentlemen, this crime not only involved one victim, but 500,000 victims, the people of the city of New Orleans. And it was an insult on our entire criminal justice system."
Improper comments by the prosecutor may constitute reversible error when the defendant's right to a fair trial is substantially affected. Causey, 185 F.3d at 417 (citing United States v. Anchondo-Sandoval, 910 F.2d 1234, 1237 (5th Cir. 1990)). Whether such error requires reversal depends upon the magnitude of the prejudicial effect, the efficacy of any cautionary instruction and the strength of the evidence of the defendant's guilt. Id. (citing United States v. Murrah, 888 F.2d 24, 28 (5th Cir.1989)). "The ultimate question before us, however, is not the impropriety of the prosecutor's remarks but whether these remarks were so inflammatory that they entitle the defendant to a new trial." United States v. Lowenberg, 853 F.2d 295, 301 (5th Cir. 1988).
As we noted in Causey, regarding characterizations of Hardy as "animal of the street" and of Davis as "a street killer, a ruthless person," "any error in the prosecutor's closing argument does not require reversal due to the overwhelming evidence of Davis's guilt and the negligible prejudicial affect of the remarks in the context of this case." Causey, 185 F.3d at 418; see also Fields, 483 F.3d at 360 (finding no plain error because, although the prosecution referred to the defendant as a "psychopath" in closing argument, "[i]n light of *683 the court's instructions and the strength of the evidence against Fields, Fields has not shown that either remark casts doubt on the correctness of the jury's verdict."). Similarly, here, there was ample evidence from which a jury could conclude that Hardy and his crew were involved in killing and that Davis counseled and protected their endeavors. Most of the prosecutor's comments in the summation referred to Hardy's involvement in Groves's murder, and were corroborated by the wiretap tapes. For example, when discussing Davis's plan of the murder, the prosecutor stated:
Hardy's going to be the executioner and they're [Davis and Williams] are going to clean it up.
...
How do you know if Sammie Williams is telling you the truth? Well, you know because you hear confirmation or corroboration of his testimony during the conversation between the defendant and his drug dealing, murdering friend, Paul Hardy, on Government's Exhibit LD-9.[8]
As stated in Part III.B., supra, the jury was already aware that Davis and Hardy had been convicted for the murder of Groves, and that Hardy was the actual shooter. Therefore, the prosecutor's remarks only argued the facts that the jury heard. Further, the district court clearly instructed the jury at the beginning and end of both phases of the re-sentencing hearings that counsel's arguments are not evidence. Accordingly, Davis's substantial rights were not affected such that reversal of his sentence is warranted.

D.
In his fourth claim, Davis complains that the victim-impact testimony and the prosecution's arguments related to that evidence were erroneous. There was no contemporaneous objection to the victim-impact testimony or the related arguments by the prosecutor, and thus the claims are reviewed for plain error. Jackson, 549 F.3d at 974-75 (testimony); Causey, 185 F.3d at 418-19 (arguments).

1.
Before Davis's re-sentencing, the Government noticed, among other nonstatutory aggravating factors: "Victim impact, evidenced by the fact that the murder of Kim Marie Groves has created harmful emotional distress upon her three children and other members of her family."[9] This aggravator was later charged to the jury as: "That the death of Ms. Groves created harmful emotional distress upon her daughter."
During the selection phase, the Government elicited sentencing testimony from the victim's daughter, Jasmine Groves, that Davis did not deserve life imprisonment because he had not "once said" he was "sorry," in "over 11 years" since the crime. Jasmine read the remarks from a letter she had written to Davis.
Prior to the August 2005 re-sentencing, and again after Jasmine's direct testimony, defense counsel obtained permission from the court to question her about a letter she and her family had sent to the United States Attorney General in June 2005. On *684 cross-examination, Jasmine acknowledged that the letter, signed by her, her two siblings, and her grandparents, had asked the Government not to pursue a capital re-sentencing for Davis but rather to allow him to receive life imprisonment. She testified that the request had been made "[s]o it can be over" and so Davis "could spend the rest of his life thinking about what he did."[10]
On redirect, the prosecutor then asked Jasmine to explain why she had thought a life sentence "would mean things would end." She answered that she had believed it would mean "no more court, no more nothing." "But," she said she had now learned, "he can keep appealing and keep going through this for the rest of our life [sic]." Defense counsel did not object.
The FDPA provides that the Government may introduce as a non-statutory aggravating factor "victim impact evidence" including "oral testimony, a victim impact statement that identifies the victim of the offense and the extent and scope of the injury and loss suffered by the victim and the victim's family, and any other relevant information." 18 U.S.C. § 3593(a). As the district court held, victim-impact evidence has been upheld as constitutional. United States v. Davis, 912 F.Supp. 938, 947 (E.D.La.1996) (citing Payne v. Tennessee, 501 U.S. 808, 111 S.Ct. 2597, 115 L.Ed.2d 720 (1991)); Bernard, 299 F.3d at 477-78 (same). Evidence "about the victim and about the impact of the murder on the victim's family is relevant to the jury's decision as to whether or not the death penalty should be imposed [and t]here is no reason to treat such evidence differently than other relevant evidence is treated." Payne, 501 U.S. at 827, 111 S.Ct. 2597. However, admission of the evidence violates Davis's due process rights if it "is so unduly prejudicial that it renders the trial fundamentally unfair." Bernard, 299 F.3d at 477 (citing Payne, 501 U.S. at 825, 111 S.Ct. 2597).
Here, the Government permissibly presented testimony from Jasmine regarding the impact of her mother's death on her family. The letter she read into testimony was part of that impact. The testimony did not render the trial "fundamentally unfair," as Davis's counsel was able to cross-examine Jasmine (and to ask leading questions). Moreover, the testimony of a single family member was not sufficient to render the trial unfair, relative to the overwhelming evidence against Davis. See Bernard, 299 F.3d at 479-81 (holding that error in admitting minimal victim impact testimony in which victim's mother directly addressed defendants did not affect substantial rights in light of the impact on the family); see also Griffith v. Quarterman, 196 Fed.Appx. 237, 245 (5th Cir.2006) (per curiam, unpublished) (in a habeas case, rejecting Due Process challenge to admissibility of victim impact evidence where only one witness (victim's brother) testified and prosecutor made only passing reference to testimony in closing argument); cf. United States v. Rodriguez, 581 F.3d 775, 796-97 (8th Cir.2009) (holding that testimony of six victim-impact witnesses was not overwhelming where witnesses explained the impact of the victim's murder on their lives and defendant presented mitigation witnesses). The victim-impact testimony here did not violate Davis's due process rights.

2.
In summation at the close of the selection phase, the prosecutor returned to *685 Jasmine's testimony to argue "the family's wishes":
"In simple and powerful words, she [Jasmine] told you that life was too good for the defendant and she told you why. He didn't have the decency to apologize. And he doesn't care, she said. And she is right. For if the defendant thinks of Kim Groves at all, it is only to ponder how he could have done this murder better. That's how he thinks of her."
Davis argues that his constitutional privilege against self-incrimination was violated by the italicized remarks, which highlighted his silence (particularly because he was absent from the proceedings).
The Fifth Amendment prohibits a prosecutor from commenting on a defendant's failure to testify, Griffin v. California, 380 U.S. 609, 615, 85 S.Ct. 1229, 14 L.Ed.2d 106 (1965), if "the prosecutor's manifest intent in making the remark must have been to comment on the defendant's silence, or the character of the remark must have been such that the jury would naturally and necessarily construe it as a comment on the defendant's silence." Jackson v. Johnson, 194 F.3d 641, 652 (5th Cir.1999) (citing United States v. Grosz, 76 F.3d 1318, 1326 (5th Cir.1996)). "The prosecutor's intent is not manifest if there is some other, equally plausible explanation for the remark." Grosz, 76 F.3d at 1326. As for whether a jury would naturally and necessarily construe a remark as a comment on the defendant's failure to testify, "the question is not whether the jury possibly or even probably would view the challenged remark in this manner, but whether the jury necessarily would have done so." Id. (quoting United States v. Collins, 972 F.2d 1385, 1406 (5th Cir. 1992)).
In Mitchell v. United States, 526 U.S. 314, 119 S.Ct. 1307, 143 L.Ed.2d 424 (1999), the Supreme Court held that a sentencing court may not draw an adverse inference from a defendant's silence "in determining the facts of the offense" because to do so "impose[s] an impermissible burden on the exercise of the constitutional right against compelled self-incrimination." Id. at 330, 119 S.Ct. 1307. Here, the prosecutor restated Jasmine's testimony that Davis never apologized in the context of discussing the family's wishes (and how they changed from wanting a life sentence to wanting the death penalty). This plausible explanation makes it debatable as to whether the remarks were intended to comment on Davis's failure to testify in the sentencing hearing. The fact that Davis was not present during the selection phase when the prosecutor made the remarks, however, could have led the jury to believe that the Government was highlighting Davis's failure to apologize.
However, the cases Davis cites in support of this argument are distinguishable. In Lesko v. Lehman, 925 F.2d 1527 (3d Cir.1991), for example, the defendant testified regarding biographical information in the mitigation phase, and the prosecutor impermissibly used that testimony to argue that he should have said more, including that he was sorry. Id. at 1540. Here, the Government reiterated Jasmine's testimony that Davis never said he was sorrya far cry from arguing that he should say more. And in Beardslee v. Woodford, 358 F.3d 560 (9th Cir.2004), the court found that the prosecutor's comments were impermissible under Griffin, but held that the error was harmless because the comments were not extensive and did not stress lack of remorse to the jury. Id. at 587. Here, the prosecutor's comments regarding Jasmine's testimony comprised a few lines of transcript in a lengthy summation, and were the only prosecutorial remarks which referred to Davis's supposed lack of remorse. The jury was already *686 aware of the wiretap tapes in which Davis celebrated Groves's death, which suggested lack of remorse. See Coble v. Quarterman, 496 F.3d 430, 438 (5th Cir. 2007) (rejecting ineffective assistance claim for failure to object to prosecutor's argument describing defendant as "remorseless" where evidence at trial showed that defendant made comments immediately after the murders that indicated his lack of remorse). In the context of the prosecutor's summation and the evidence overall, therefore, Davis's rights were not affected by the isolated remark.

E.
In his fifth claim, Davis argues that the prosecution's closing arguments at the selection phase of the sentencing hearing were improper and constitute reversible error.[11] Davis specifically takes issue with five categories of statements.
First, during closing arguments at the selection phase, prosecutors stated that sentencing Davis to life imprisonment for his convictions under 18 U.S.C. §§ 241 and 242 would not, as a practical matter, punish him for those offenses because he was already serving a life sentence on an earlier drug conspiracy offense.[12] In rebuttal summation, the prosecutor also stated: "But more importantly, as [defense counsel] told you, if you don't sentence him to death, this murder is a freebie. Don't do that."
Second, the prosecutor commented on the jurors' duty to return a death sentence, even if mitigation evidence is presented:
You see, some crimes, some defendants deserve the death penalty. Let's get back to why we're here. This defendant deserves it. When a police officer murders a citizen in cold blood in retaliation for making a complaint against him, it always deserves the death penalty, period, without exception.[13]
*687 Third, the prosecutor referred to the effects of Davis's actions on the broader community.[14] The prosecutor also told jurors that they "speak for [Kim Groves]," asked jurors to return a death sentence "for every tear that Jasmine Groves cried," and urged that "Jasmine Groves waits for you to give her justice."
Fourth, in rebuttal closing summation, the prosecutor repeatedly described Davis as "evil" and described defense counsel as follows:
Counsel talked to you in the beginning of his closing argument about killing. How dare he compare your dedication, your willingness to follow your sworn duty with the murderous rampage of Len Davis. It is a cheap trick and he is attempting to manipulate you. Don't let him.
Finally, the prosecutor argued other facts, such as "[t]he death penalty was an act [sic] for murderers like this and murderers like Len Davis. You will never see a more cold, calculated killing." This remark is the only one to which defense counsel objected. The district court overruled his objection.
Because Davis did not object to the first four categories of comments in the prosecutor's closing argument, we apply only plain error review. Fields, 483 F.3d at 360. First, as to the prosecutor's argument that a life sentence would not be adequate punishment because Davis was already serving a life sentence for drug offenses, we conclude that any failure by the district court to correct the remarks was not plain error. Courts have divided on the question of whether such an argument is permissible. Compare, e.g., People v. Kuntu, 196 Ill.2d 105, 256 Ill.Dec. 500, 752 N.E.2d 380, 403 (2001) ("We find error in allowing the State to argue to the jury that, if it should fail to vote to sentence defendant to death, the jury will be giving the jury five free murders."), with Rodden v. Delo, 143 F.3d 441, 447 (8th Cir.1998) ("In context, the prosecutor's statement about the second murder being free urged the jury to impose additional punishment for the additional crime.... The jury could properly consider [the defendant]'s earlier crimes in deciding whether to sentence him to death."). Given the contradictory authority, and our lack of circuit precedent on the issue, the district court's error, if any, was not clear or obvious. See United States v. Scroggins, 599 F.3d 433, 450 (5th Cir.2010) (refusing to find plain error in light of divided legal authorities).
In addition, the prosecutor's remarks did not communicate to jurors that they were legally bound to impose the death penalty or that they could not consider Davis's mitigating factors. The jurors were instructed to the contrary by the court immediately before their deliberations, and were informed that the arguments were just thatnot evidence. *688 Moreover, there was not inappropriate disparagement of Davis or defense counsel. See Causey, 185 F.3d at 418. The remarks were drawn from evidence in the record and could be inferred from the evidence the jury heard. See United States v. Mendoza, 522 F.3d 482, 491 (5th Cir.2008) (stating that a prosecutor "is confined in closing argument to discussing properly admitted evidence and any reasonable inferences or conclusions that can be drawn from that evidence"). Davis cannot demonstrate that the remarks prejudiced him.
As to the fifth type of remark to which Davis objected, in which the prosecutor characterized him as a "cold-blooded killer," the district court did not abuse its discretion in overruling the objection. Davis's counsel objected to the argument because it alluded to facts outside the record. This was in direct response to the court's sustaining his objection to the prosecutor's mention of other criminal cases in the Government's summation. Here, the remark was not directed to facts outside the record or unrelated to the evidence introduced at trial. While the "prosecutor would have done well to refrain from making certain ... statements," see Johnson v. Bagley, 544 F.3d 592, 598 (6th Cir.2008), the isolated remarks do not cast serious doubt on the correctness of the jury's verdict. Fields, 483 F.3d at 360.
Davis directs us to Sinisterra v. United States, 600 F.3d 900 (8th Cir.2010), in support of his claim. In Sinisterra, a federal habeas petitioner challenged the prosecutor's closing argument in which the jury was urged to "act as the conscience of the community and `send a message to all other drug dealers that this community will not tolerate [crimes like the petitioner's].'" 600 F.3d at 910. The Eighth Circuit held that by urging the jury to impose a death sentence to send a message to other criminals, the prosecutor "impinge[d] upon the jury's duty to make an individualized determination that death is the appropriate punishment for the defendant." Id. Sinisterra is distinguishable from the facts here, where the prosecution did not urge the jury to send a message to other criminals. Moreover, we have previously held that "[a]though the prosecution may not appeal to the jury's passions and prejudices, the prosecution may appeal to the jury to act as the conscience of the community." Jackson, 194 F.3d at 655 & nn. 54-56. This is precisely what the prosecution did here. Therefore, Davis suffered no prejudice.

F.
In his sixth claim, Davis argues that the district court abused its discretion in instructing the jury on the "substantial planning and premeditation" aggravating factor under 18 U.S.C. § 3592(c)(9).[15]
Before re-sentencing, the defense proposed the following written jury instruction, in relevant part, regarding the "substantial planning and premeditation" aggravating factor submitted by the Government:
Substantial Planning and Substantial Premeditation
...
A premeditated murder is one committed upon deliberation and prior design. In short, the government must prove beyond a reasonable doubt that the defendant killed Kim Groves while acting under color of law only after thinking the matter over and deliberating whether to act. There is no requirement *689 that the government prove that the defendant deliberated for any particular period of time in order to show premeditation. It must, however, show that the defendant had a considerable period of time to become fully aware of what he intended to do and to think it over before he acted.
The government must also establish beyond a reasonable doubt that the murder was committed after substantial planning for you to find this element proved. The words "substantial planning" should be given their ordinary, every day meaning. "Substantial planning and premeditation" is not established by simply showing that a murder was premeditated, nor that some small amount of planning preceded it. Rather, it must be shown that there was both a considerable or large amount of premeditation and there was a considerable or large amount of planning preceding the murder.
The district court rejected this proposed instruction. The final instruction to the jury read, in relevant part:
A killing is committed after substantial premeditation when it is committed upon substantial deliberation. In short, the government must prove the defendant killed Kim Groves only after substantially thinking the matter over and deciding to do it beforehand. There is no requirement that the government prove that the defendant deliberated for any particular period of time in order to show substantial premeditation. It must, however, show that the defendant had enough time to become fully aware of what he intended to do and to substantially think it over before he acted.
The government must also establish beyond a reasonable doubt that the killing was committed after substantial planning for you to find this factor proved. "Planning" means mentally formulating a method for doing something or achieving some end. The words "substantial planning" should be given their ordinary, everyday meaning. "Substantial" planning requires a considerable amount of planning preceding the killing.
The court overruled Davis's objection to the instruction that, to prove premeditation, "[t]here is no requirement that the government prove that the defendant deliberated for any particular period of time." The jury ultimately found this factor proven beyond a reasonable doubt for each of the two counts of conviction.
Because "[d]istrict courts enjoy substantial latitude in formulating a jury charge," we review "all challenges to, and refusals to give, jury instructions for abuse of discretion." United States v. Webster, 162 F.3d 308, 321-22 (5th Cir. 1998), cert. denied, 528 U.S. 829, 120 S.Ct. 83, 145 L.Ed.2d 70 (1999). "A refusal to give a requested instruction constitutes reversible error only if the proposed instruction (1) is substantially correct, (2) is not substantively covered in the jury charge, and (3) pertains to an important issue in the trial, such that failure to give it seriously impairs the presentation of an effective defense." Id. Ambiguous jury instructions in the capital context warrant reversal only if "there is a reasonable likelihood that the jury has applied the challenged instruction in a way that prevents the consideration of constitutionally relevant evidence." Boyde v. California, 494 U.S. 370, 380, 110 S.Ct. 1190, 108 L.Ed.2d 316 (1990).
In United States v. Flores, 63 F.3d 1342 (5th Cir.1995), we construed the word "substantial" as used in the "substantial planning and premeditation" aggravator "to denote a thing of high magnitude." 63 F.3d at 1373. Accordingly, "the term alone, without further explanation, [is] sufficient *690 to convey that meaning and to enable the jury to make an objective assessment." Id. at 1374. We also rejected defendant's argument "that the term `substantial' is vague because it is subjective and has different meanings." Id. at 1373.
Here, the proposed instruction for "a considerable or large" amount of planning is substantively covered in the final jury charge, where "substantial planning" is defined as requiring "a considerable amount of planning preceding the killing." As for the definition of "substantial premeditation," there is no reasonable likelihood that the jury would have applied the instruction in a way that prevented consideration of evidence. The charge, "[t]here is no requirement that the government prove that the defendant deliberated for any particular period of time," was given in the context of the remaining elements of the charge, including, "[i]t must, however, show that the defendant had enough time to become fully aware of what he intended to do and to substantially think it over before he acted." Given that the term "substantial" could have denoted "a thing of high magnitude" on its own, the remaining elements of the jury charge served to underscore that definition. See Flores, 63 F.3d at 1373-74. Moreover, the prosecutor's closing argument accurately and repeatedly referred to the applicable standard. Accordingly, the district court did not abuse its discretion in refusing to incorporate Davis's proposed instruction.

G.
In his seventh claim, Davis asserts that the district court committed plain error in instructing the jury on mitigating evidence or in drafting the verdict forms on the same. Because Davis failed to object to the verdict forms or the portion of the jury instructions pertaining to mitigation, this court reviews for plain error. Jones, 527 U.S. at 388-89, 119 S.Ct. 2090.
Shortly before Davis's re-sentencing hearing, the defense proposed sixteen mitigating factors for submission to the jury, listed here in relevant part:
1. Other participants in one or more of the capital offenses who are equally or more culpable than Len Davis will not be punished by death, including, but not necessarily limited to, the following individuals: Sammie Williams, Steven Jackson [driver of the getaway vehicle], Damon Causey.
2. Other participants in the capital offenses received reduced sentences as a result of plea agreements with the government.
...
4. Other participants in the drug trafficking conspiracy are now eligible to receive reduced sentences as a result of their testimony against Mr. Davis and plea agreements with the government.
5. Sammie Williams is equally or more culpable than Len Davis and he will not be punished by death.
...
7. As a police officer, Len Davis intervened and persuaded a woman who was threatening to commit suicide and/or kill him and his partner to surrender her gun.
8. On several occasions, Len Davis answered calls for assistance from fellow officers who were being shot at and assisted in apprehension of the suspects, putting his own life in danger to save the lives of his fellow officers.
9. While answering a fellow officer's call for assistance, Len Davis joined *691 in the chase of 3 armed men and was shot in the stomach.
10. Len Davis was a decorated police officer and received many commendations, including a Purple Heart, while with the New Orleans Police Department.
11. Although Len Davis can distinguish right from wrong, and deserves to be held accountable for his actions, his behavior was negatively impacted by the stress of working in a high crime area.
12. Although Len Davis can distinguish right from wrong and deserves to be held accountable for his actions, his behavior was negatively impacted by the stress of being shot at on numerous occasions.
13. Although Len Davis can distinguish right from wrong and deserves to be held accountable for his actions, his behavior was negatively impacted by being shot in the stomach while coming to the assistance of fellow officers.
In drafting the jury instructions and verdict forms, the district court condensed the individual factors to seven categories of mitigating factors that were submitted to the jury with the instruction that they were to "indicate the number of jurors who find the factor established by a preponderance of the evidence" as to each count of the conviction. See 18 U.S.C. § 3593 (listing burden of proof for mitigating factors). The categories at issue here relate to: (1) Davis's good character evidence (proposed factors 7, 8, 9, and 10); (2) the culpability and relatively lenient punishment imposed on other individuals involved in Groves's murder and the drug conspiracy (factors 1, 2, 4, and 5); and (3) the stressful and dangerous conditions of his job (proposed factors 11, 12, and 13). The final list of factors included the following, in relevant part:
A. Other participants in one or more of the capital offenses who are equally or more culpable than Len Davis will not be punished by death, including, but not necessarily limited to, the following individuals: Sammie Williams, Steven Jackson, Damon Causey. Other participants in the capital offenses received reduced sentences as a result of plea agreements with the government. Other participants in the drug trafficking conspiracy are now eligible to receive reduced sentences as a result of their testimony against Mr. Davis and plea agreements with the government.
C. As a police officer, Len Davis frequently risked his own life to apprehend criminal suspects, assist fellow officers and save innocent victims. Len Davis was a decorated police officer and received many commendations, including a Purple Heart, while with the New Orleans Police Department.
D. Although Len Davis can distinguish right from wrong and deserves to be held accountable for his actions, his behavior was negatively impacted by the stress of working in a high crime area, being shot at on numerous occasions, including on one occasion being shot in the stomach while coming to the assistance of fellow officers.
The verdict form also included a "catch-all" category:
G. Other factors in Len Davis's background or character mitigate against imposition of a death sentence.
Similarly, the court instructed the jury that:

*692 [t]he law permits you to consider anything about the commission of the crime or about Mr. Davis' background or character that would mitigate against the imposition of the death penalty. Thus, if there are any such mitigating factors, whether or not specifically argued by defense counsel, but which are established by a preponderance of the evidence, you are free to consider them in your deliberations.
(emphasis added). No juror found any mitigating factor.
The Eighth Amendment requires that, in a capital case, the sentencing jury be able to consider and give effect to the defendant's mitigating evidence. Penry v. Johnson, 532 U.S. 782, 797, 121 S.Ct. 1910, 150 L.Ed.2d 9 (2001). In determining whether the jury instructions impermissibly limited consideration of mitigating evidence, an appellate court must ask whether there is "a reasonable likelihood that the jurors ... understood the challenged instructions to preclude consideration of relevant mitigating evidence proffered by [the defendant]." Buchanan v. Angelone, 522 U.S. 269, 279, 118 S.Ct. 757, 139 L.Ed.2d 702 (1998) (quoting Boyde v. California, 494 U.S. 370, 386, 110 S.Ct. 1190, 108 L.Ed.2d 316 (1990)).
Here, each of the seven mitigating factors derived from the fact-specific individual factors proposed by the defense. Factor "G." on the verdict form, the "catch-all" factor, permitted the jury to consider whether "[o]ther factors in Len Davis's background or character mitigate against imposition of a death sentence," thereby covering any factors that had been condensed. Further, the jury was not unaware of the facts underlying the mitigating factorsfor example, that Davis was injured in the line of duty while aiding fellow officersbecause they had heard the mitigation evidence presented during the selection phase of the re-sentencing. Thus, there is no "reasonable likelihood that the jurors understood the challenged instructions to preclude consideration of relevant mitigating evidence." Buchanan, 522 U.S. at 279, 118 S.Ct. 757. In addition, the court's instructions regarding consideration of mitigation evidence ensured that the jurors considered the mitigation factors correctly. Millsaps, 157 F.3d at 993 ("[J]uries are presumed to follow their instructions."); see also Flores, 63 F.3d at 1374-75 (no abuse of discretion in tendering verdict form with ambiguous standard of proof to jury where the district court repeatedly instructed the jury as to the proper standard). Davis's substantial rights were not affected such that a reversal of his sentences is warranted.

IV.
Davis seeks reversal not only of his death sentences under the FDPA, but also of his convictions. We examine the seven claims related to his convictions in turn, keeping in mind that we affirmed Davis's convictions in his first appeal. See Causey, 185 F.3d at 412-21.

A.
Davis first raises a challenge under Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986) to the jurors selected in his 1996 trial. During that jury selection, the prosecution used peremptory challenges to remove nine of ten African-American women and two of four African-American men from the pool of qualified jurors from which the 12-member jury was selected. Although the trial court failed to find a prima facie case of discrimination, it asked the prosecution to provide reasons for the strikes and, following the government's proffer and the defense's response, overruled the Batson challenges.
*693 Our review of this claim is foreclosed under the "law of the case" doctrine. In other words, "an issue of fact or law decided on appeal may not be reexamined either by the district court on remand or by the appellate court on a subsequent appeal." United States v. Williams, 517 F.3d 801, 806 (5th Cir.2008) (citation omitted); accord United States v. Cervantes-Blanco, 504 F.3d 576, 587 (5th Cir. 2007); United States v. Becerra, 155 F.3d 740, 752 (5th Cir.1998), abrogated on other grounds as stated in United States v. Farias, 481 F.3d 289, 292 (5th Cir.2007). "This prohibition covers issues decided both expressly and by necessary implication, and reflects the jurisprudential policy that once an issue is litigated and decided, that should be the end of the matter." United States v. Pineiro, 470 F.3d 200, 205 (5th Cir.2006) (citation and internal quotation marks omitted).
This court has recognized three exceptions to the law-of-the-case doctrine. "[A] prior decision of this [C]ourt will be followed without reexamination ... unless (i) the evidence on a subsequent trial was substantially different, (ii) controlling authority has since made a contrary decision of the law applicable to such issues, or (iii) the decision was clearly erroneous and would work a manifest injustice." Williams, 517 F.3d at 806-07 (citations omitted); Becerra, 155 F.3d at 752-53.
We rejected Davis's Batson challenge in his first appeal. Causey, 185 F.3d at 413 (holding that the Government's explanations for their peremptory strikes were race neutral and not outside the realm of credibility) (citing Purkett v. Elem, 514 U.S. 765, 768, 115 S.Ct. 1769, 131 L.Ed.2d 834 (1995)).[16] Here, Davis presents arguments regarding strikes against seven African-American jurors, the same jurors whose strikes he appealed to the district court and to this court in Causey. Accordingly, the law of the case doctrine precludes review of his claim in this appeal.
Davis argues that intervening case law has created a contrary decision of the applicable law such that the law of the case doctrine does not apply. Specifically, Davis argues that Miller-El v. Dretke, 545 U.S. 231, 125 S.Ct. 2317, 162 L.Ed.2d 196 (2005) and Snyder v. Louisiana, 552 U.S. 472, 128 S.Ct. 1203, 170 L.Ed.2d 175 (2008) establish that the district court erred in overruling his Batson challenges. Additionally, he asserts, we applied an incorrect standard of review in affirming his Batson claim in his first appeal.
Davis's arguments have no merit. In Miller-El, a habeas case, the Supreme Court ruled that a Batson violation had occurred because another panel of this court had failed to thoroughly review the voir dire record to determine the plausibility of the state prosecutor's reasons for striking African American jurors. Miller-El, 545 U.S. at 251-52, 125 S.Ct. 2317. Davis argues that Miller-El established that a comparative juror analysis is the centerpiece of a Batson claim. In Murphy v. Dretke, 416 F.3d 427 (5th Cir.2005), cert. denied, 546 U.S. 1098, 126 S.Ct. 1028, 163 L.Ed.2d 868 (2006), decided shortly after Miller-El, we determined that Miller-El did not change controlling law:
[T]he [Miller-El] Court considered the type and quantum of record evidence required to demonstrate a Batson violation. The Court did not announce any new elements or criteria for determining a Batson claim, but rather simply made a final factual and evidentiary determination *694 of that particular petitioner's Batson claim pursuant to the "demanding but not insatiable" standard set forth in [the relevant statutory provisions governing habeas review].
416 F.3d at 439 (internal citations omitted). In Snyder, a direct appeal from state court, the Supreme Court found a Batson violation when the state court failed to make a finding on the record either crediting or denying the prosecutor's reasons for challenges to African American jurors. 552 U.S. at 484-85, 128 S.Ct. 1203. This holding did not change the law of review of peremptory challenges, and we reject Davis's attempts to mischaracterize Snyder.
Davis also argues that our standard of review in his first appeal is clearly erroneous in light of Snyder and Miller-El. This argument is also unavailing. In Davis's first appeal, we stated, "the district court's decision on the ultimate question of discrimination is a fact finding, which is accorded great deference." Causey, 185 F.3d at 413. Miller-El does not even address the standard of review.[17] And Snyder, in fact, restates the same standard: "On appeal, a trial court's ruling on the issue of discriminatory intent must be sustained unless it is clearly erroneous." 552 U.S. at 477, 128 S.Ct. 1203. Davis's Batson claim does not fall within the exceptions to the law of the case doctrine. Accordingly, review of this issue is foreclosed.

B.
Next, Davis urges that the Government withheld material evidence about Williams in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963) and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972).
At Davis's 1996 trial, Williams testified on direct that he had pleaded guilty to two felony weapons and drug possession charges in connection with the FBI's Operation Shattered Shield. Upon questioning by the prosecutor, he told jurors he was facing a mandatory five-year sentence and "possible life sentence in prison" on those charges. The prosecutor then asked Williams:
Q. Now, in connection with your guilty plea, sir, did you have an agreement, written or otherwise, with the government?
A. No, I didn't have any agreement.
Then, the prosecutor asked Williams about his sentence, which was still pending at the time of his testimony:
Q. Now, you pleaded "guilty" just about a year ago. Any reason why you haven't been sentenced yet, to your knowledge?
A. Yes. Me and my attorney asked the judge[18] to allow us the opportunityallow me the opportunity to cooperate before being sentenced.
...
Q. What do you hope to get out of your testimony?
A. Well, I'm hoping the government informs the judge of my cooperation *695 and, as a result, he [the sentencing judge] will give me a lesser sentence than he otherwise may impose on me.
Q. Has the governmenthave I or any government attorney promised you anything?
A. No.
Q. Has anyoneby that I mean either the government, any government attorney or [the sentencing judge] made any prediction as to what your sentence could possibly be?
A. No.
On cross-examination, Williams reiterated that he did not have an agreement with the Government. Defense counsel asked Williams about a "5K letter," a motion for downward sentence departure pursuant to U.S.S.G. § 5K1 in which the Government informs the sentencing judge of a witness's cooperation. Williams was familiar with the letter, and that the Government told him "they can do that"i.e., file the 5K letterbut "[t]hey didn't guarantee me that they would or would not either."
In 2001, after we remanded for re-sentencing, Davis filed a motion to obtain Williams's plea agreement pursuant to Brady and Giglio. Davis stated that trial testimony from FBI personnel revealed that Williams was promised witness protection for himself and his family in exchange for his cooperation, and that the Government would consider filing the 5K letter for Williams. In reply, the Government stated that Williams's request for a plea agreement was rejected, but if he cooperated without an agreement, witness protection would be made available. If the cooperation was substantial, the Government would consider filing the 5K letter, but neither the letter nor a lighter sentence were guaranteed. The district court conducted an evidentiary hearing in May 2001, during which it heard testimony from Williams, his attorney, and the assistant U.S. attorney from whom Williams's attorney requested a plea agreement. At the conclusion of the hearing, the court agreed with the prosecutor that new information could be brought out at re-sentencing if Williams testified. In the minute entry filed after the hearing, the district court stated it "consider[ed] the Motion to have been satisfied."
After we remanded a second time for re-sentencing, Davis filed a renewed Brady motion, arguing that the Government's failure to disclose Williams's agreement entitled Davis to a new trial as to his guilt or innocence. At the hearing on the motion in May 2005, Davis[19] argued that Williams's trial testimony demonstrated discrepancies consistent with a Brady violation. The district court replied that she had two "fundamental" problems with the motion. The first was "purely procedural" because Davis's convictions had been affirmed by this court on direct appeal. Therefore, the district court did not believe she had the authority to do anything about the motion "other than deny it on procedural grounds." The court also stated that she did not agree that the discrepancies Davis relied on were "particularly significant." Davis then argued that his convictions for Counts 1 and 2 of the indictment had been overturned when this court vacated the death sentences and remanded for re-sentencing. The district court corrected this error: "[Y]our convictions were affirmed. So I don't think I can do anything about ordering a new trial on your guilt phase." When Davis reiterated his Brady claim, the court stated, "But even if I were to get to the merits of your motion, I'm not persuaded that *696 there's anything significant here thatsignificant enough that justifies a new trial."
Brady/Giglio claims raised in a motion for a new trial are reviewed de novo. United States v. Fernandez, 559 F.3d 303, 319 (5th Cir.), cert. denied, ___ U.S. ___, 129 S.Ct. 2783, 174 L.Ed.2d 273 (2009). While we examine the Brady question de novo, "we must proceed with deference to the factual findings underlying the district court's decision." United States v. Severns, 559 F.3d 274, 278 (5th Cir.2009).
Brady prohibits the Government from suppressing evidence favorable to the accused "where the evidence is material either to guilt or to punishment." Brady, 373 U.S. at 87, 83 S.Ct. 1194. When a defendant seeks a new trial on the basis of a Brady violation, he must show that "(1) the prosecution did not disclose the evidence; (2) the evidence was favorable to the defense; and (3) the evidence was material." Fernandez, 559 F.3d at 319 (quoting United States v. Infante, 404 F.3d 376, 386 (5th Cir.2005)). Evidence is "material" if there is "a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Severns, 559 F.3d at 278 (citation omitted). A "reasonable probability" is a probability sufficient to undermine confidence in the outcome. Id. (citations omitted).
Giglio applies the Brady rule to evidence affecting the credibility of key government witnesses. 405 U.S. at 154-55, 92 S.Ct. 763. "A Giglio violation usually occurs when a cooperating witness denies having a plea agreement and the prosecutor fails to correct the misstatement." United States v. Williams, 343 F.3d 423, 439 (5th Cir.), cert. denied, 540 U.S. 1093, 124 S.Ct. 966, 157 L.Ed.2d 800 (2003). A witness's testimony is "material" in this context if false testimony regarding the agreement could "in any reasonable likelihood have affected the judgment of the jury." Giglio, 405 U.S. at 154, 92 S.Ct. 763 (internal quotation marks omitted).
Under either standard, Davis's claims fail. Davis argues that Williams had an undisclosed plea agreement. The evidence reflects, however, that Williams had discussed a plea agreement with the Government, but did not have an actual agreement in place at the time of his 1996 testimony. At the May 2001 hearing on Davis's Brady motion, Williams reiterated under oath that he did not have an agreement. The FBI agents who testified at the same hearing stated that they assumed Williams had an agreement, and indicated as such in their summaries of interviews with him after his arrest. However, they also stated that they had never been told by Williams or by government attorneys that Williams actually had a plea agreement. Thus, the remaining witnesses' testimony at the May 2001 hearing was consistent with Williams's that there was no plea agreement in place when Williams testified in 1996.
Even if there was an undisclosed agreementfor example, if the offer of witness protection can be considered an agreementDavis still cannot show "a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Severns, 559 F.3d at 278. The information about the witness protection was not favorable to Davis because the jury may have assumed that Williams needed protection from Davis, who allegedly had Groves killed for filing a complaint against him. Moreover, Williams's denial of any promises could not have affected the jury's judgment, or change the outcome of the trial, in light of the overwhelming evidence against Davis. See *697 United States v. Sipe, 388 F.3d 471, 478 (5th Cir.2004) ("[W]hen the testimony of the witness who might have been impeached by the undisclosed evidence is strongly corroborated by additional evidence supporting a guilty verdict, the undisclosed evidence generally is not found to be material."). The Brady/Giglio claim was correctly dismissed.

C.
Next, Davis argues that the evidence was insufficient to prove the "color of law" element of Counts 1 and 2 of the indictment. We rejected this claim in Davis's first appeal. Causey, 185 F.3d at 413-16; see also id. at 433-44 (Dennis, J., concurring) (discussing arguments in support of conviction under 18 U.S.C. §§ 241 and 242). Therefore, the law of the case doctrine applies to foreclose review in this appeal. Williams, 517 F.3d at 806.
Notwithstanding our binding precedent, Davis asserts that the Supreme Court's ruling in United States v. Morrison, 529 U.S. 598, 120 S.Ct. 1740, 146 L.Ed.2d 658 (2000) is intervening case law that brings the issue within the exception to the law of the case doctrine. He is incorrect. In Morrison, the Supreme Court held that a portion of the Violence Against Women Act, 42 U.S.C. § 13981, which provided a private cause of action for victims of gender-motivated violence, was not a valid exercise of Congress's authority under Section 5 of the Fourteenth Amendment. 529 U.S. at 627, 120 S.Ct. 1740. Contrary to Davis's assertions, Morrison did not change the standard for determining whether conduct qualifies as "state action," which here is synonymous with action "under color of law." Rather, Morrison addressed Congress's constitutional authority to prohibit purely private conduct that does not qualify as state action or action under color of law. Therefore, it is not a relevant intervening change of law, and this issue does not fall within the exceptions to the law of the case doctrine. See Cervantes-Blanco, 504 F.3d at 587 ("Even if we were to reconsider Cervantes's objection, there has been no change in Supreme Court or circuit law that would permit us to reverse the district court."); United States v. McCrimmon, 443 F.3d 454, 461-62 (5th Cir.2006). Accordingly, this court's review of this claim is foreclosed.

D.
Fourth, Davis asserts that omission of the FDPA elements from the indictment precluded the government from seeking the death penalty at re-sentencing. As Davis acknowledges, we addressed this issue in response to the Government's previous appeals from a district court ruling. United States v. Davis, 380 F.3d 821 (5th Cir.2004); reh'g & reh'g en banc denied, 121 Fed.Appx. 59 (5th Cir.2004) (table), cert. denied, 544 U.S. 1034, 125 S.Ct. 2245, 161 L.Ed.2d 1062 (2005). Specifically, we held that omission of the FDPA elements from the indictment was harmless error, and overruled the district court's findings to the contrary. Id. at 829-30 (citing United States v. Robinson, 367 F.3d 278, 284-85, 287 (5th Cir.2004)). Davis does not and cannot argue that this issue falls within the exceptions to the law of the case doctrine; therefore, review is foreclosed. See Williams, 517 F.3d at 806; McCrimmon, 443 F.3d at 461-62.

E.
Fifth, Davis claims that the Double Jeopardy Clause precludes his conviction for violating both 18 U.S.C. §§ 241 and 242. Specifically, Davis argues that his conviction for violating Groves's civil rights was a lesser-included offense of his *698 conviction for conspiring to violate her civil rights. In his view, the convictions violate double jeopardy, and one of them must be struck.
We need not address the Government's argument that Davis waived this claim, because the claim was foreclosed when we affirmed Davis's convictions under Sections 241 and 242 in his first direct appeal. Causey, 185 F.3d at 413-16. Additionally, no exceptions to the law of the case doctrine apply. McCrimmon, 443 F.3d at 461-62.

F.
Next, Davis asserts that the indictment erroneously alleged a deprivation of the right to "liberty" rather than a deprivation of the right to "life." Davis argues that the "death resulting" element of each charge meant he was effectively prosecuted for murder, even though the constitutional right he allegedly deprived the victim of, according to the indictment, was the right to liberty, not the right to life.
Review of this issue is foreclosed because Davis's conviction on both counts, based on sufficient evidence, was affirmed in his first appeal. See Causey, 185 F.3d at 438 (Dennis, J., concurring) ("Arguably, a person also has a separate `defined right' protected by the Constitution not to be deprived of liberty without due process of law, and this right is also violated by having his or her life taken willfully by a state officer acting under color of law."); see also id. at 438-44 (discussing cases). We also find that no exceptions to the law of the case doctrine apply. McCrimmon, 443 F.3d at 461-62.

G.
Finally, Davis claims that the Supreme Court's decisions in Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000) and Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002) resulted in an unconstitutional judicial rewriting of 18 U.S.C. §§ 241 and 242.
Davis argues that though Apprendi and Ring forbid treating the "death resulting" requirement as a sentencing factor, treating it as an element of the indictment amounts to a judicial rewriting of the underlying criminal statutes, in violation of the Separation of Powers doctrine and the constitutional prohibition on ex post facto laws.
Davis's briefing on this point consists of a single paragraph in which he references his unsuccessful motion to the district court. This briefing is insufficient for the purposes of Federal Rule of Appellate Procedure 28(a), and therefore the issue is deemed waived. See United States v. Posada-Rios, 158 F.3d 832, 867 (5th Cir. 1998), cert. denied, 526 U.S. 1031, 119 S.Ct. 1280, 143 L.Ed.2d 373 (1999) (waiving appellant's argument where it merely referenced pleadings filed in the district court without stating facts or legal authority in support).
Even if the argument were not waived, it would be unavailing on the merits. As the Government correctly notes, neither Apprendi nor Ring infringe on Congress's powers by creating new criminal offenses that did not previously exist. The rule announced in these cases simply made clear that the "death resulting" component of §§ 241 and 242 must be alleged in the indictment and found by the jury beyond a reasonable doubt. Apprendi, 530 U.S. at 490, 120 S.Ct. 2348; Ring, 536 U.S. at 609, 122 S.Ct. 2428. Further, a violation of Section 241 or 242 that results in death still carries a maximum sentence of life imprisonment or deaththe same penalty that existed before Apprendi and Ring *699 were decided. Therefore, neither decision raises any ex post facto or due process concerns. See Rogers v. Tennessee, 532 U.S. 451, 459-60, 121 S.Ct. 1693, 149 L.Ed.2d 697 (2001) (noting the fair notice concerns underlying both the Due Process and Ex Post Facto Clauses). Therefore, Davis's convictions cannot be overturned on this basis.

V.
For the foregoing reasons, we AFFIRM Davis's convictions and sentences.
AFFIRMED.
NOTES
[1]  The district court had previously severed Davis and Hardy's re-sentencing hearings. The 2005 re-sentencing jury was different from the jury that convicted Davis in 1996.
[2]  This hybrid representation resulted from motions Davis filed regarding his right to self-representation. See United States v. Davis, No. 01-30656, 2001 WL 34712238, at *3 (5th Cir. July 17, 2001) (issuing writ of mandamus that Davis be permitted to represent himself); United States v. Davis, 285 F.3d 378, 385 (5th Cir.2002) (issuing another writ of mandamus finding appointment of independent counsel violated Davis's right to self-representation).
[3]  For example, the jury heard the FBI wiretap tapes in which Davis discussed with Hardy a murder he thought Hardy had ordered:

And you can't go to jail for putting a hit on somebody, Paul. You only go to jail if you were the gunman.....You don't get charged with that kinda stupid shit over here. That shit ain't gonna fly, man. That'd be the Feds with that shit. And the only way they can prove it, they gotta have you on tape and shit.
[4]  But see United States v. McWaine, 243 F.3d 871, 873-74 (5th Cir.2001), overruled on other grounds by United States v. Cotton, 535 U.S. 625, 122 S.Ct. 1781, 152 L.Ed.2d 860 (2002) (applying the two-step analysis where the defendant did not object to prosecutor's allegedly improper remarks); United States v. Lankford, 196 F.3d 563, 573-74 (5th Cir. 1999) (same). Under this or the plain error standard, Davis's claim fails.
[5]  Williams and Duncan had been caught in Operation Shattered Shield and convicted on drug-conspiracy charges.
[6]  During the eligibility phase of the penalty proceedings, Davis represented himself with appointed back-up counsel.
[7]  Though Davis refused to be present in the courtroom during the selection phase, he permitted his back-up counsel to proceed without him.
[8]  Government Exhibit LD-9 is the wiretap excerpt of a conversation between Hardy and Davis the evening of October 13, 1994, when Davis first mentions his desire for Hardy to kill Groves.
[9]  In a pre-trial filing, Davis moved to strike this aggravating factor. The district court denied the motion, holding that victim impact evidence is relevant, admissible, and constitutional. United States v. Davis, 912 F.Supp. 938, 947 (E.D.La.1996). Davis did not appeal this ruling.
[10]  Defense counsel used these words after requesting permission from the district court to lead the witness.
[11]  The Government argues that Davis is making essentially the same argument regarding the prosecution's closing remarks as he did in his fourth claim. While we see the similarities between Davis's fourth and fifth claims, Davis challenges different types of remarks for different reasons in each claim. Given the severity of the penalty in this case, we will review the claims separately.
[12]  The prosecution stated:

He's already serving life for the cocaine conviction. If you don't return a sentence of death, you're giving him a free pass for killing Kim Marie Groves. Is that just? He won't be punished at all. And I want you to listen to what I'm saying. You give him life, you don't give him death, he won't be punished at all for killing, executing Kim Marie Groves. He gets a free pass. Is that just? Huh? Life here is no punishment at all.
... He gets life, he wins again.... [I]f you don't return a sentence of death, which is the only just sentence in this case, Len Davis will be celebrating again tonight. Don't let that happen.
[13]  The prosecutor also stated:

Do not confuse mercy with weakness. You have an obligation to uphold the law and that takes courage.
....
Certain crimes, regardless of mitigation, deserve the death penalty. The fact is so reprehensible it demands a sentence of death. You see, ladies and gentlemen, this crime not only involved one victim, but 500,000 victims, the people of the city of New Orleans. And it was an insult on our entire criminal justice system. Do not capitulate, be vigilant. Your response to his behavior cannot be tepid, it cannot be timid, it must be certain and it must be in kind and it must express our outrage and unyielding commitment to the rule of law.
....
[Len Davis] deserves justice and justice can only be had in this case if the death penalty is imposed.... [Y]ou are the dispensers of justice in this particular case. Jasmine Groves waits for you to give her justice. The citizens of the City of New Orleans wait for you to give them justice. And justice can only be had by sentencing Len Davis to death. For if not him, who? If not now, when? If a policeman killing a citizen using a drug dealer that he is protecting is not enough, then what is?
[14]  Examples of the remarks include:

He prayed [sic] on a community, this community, New Orleans, Louisiana, in the Eastern District of Louisiana that desperately needed, still needs protection from the likes of Len Davis.
....
If you want to shed a tear, shed a tear for the city of New Orleans. The city of New Orleans had to endure the reign of terror of Len Davis and the murderers he was protecting. And if you want to shed a tear, cry for all of the people who are denied justice because Len Davis was protecting those persons who victimized them.
[15]  The factor states, in relevant part, "The defendant committed the offense after substantial planning and premeditation to cause the death of a person." 18 U.S.C. § 3592(c)(9).
[16]  We also denied Davis's petitions for rehearing and rehearing en banc in November 1999. The Supreme Court denied certiorari. Causey v. United States, 530 U.S. 1277, 120 S.Ct. 2747, 147 L.Ed.2d 1010 (2000).
[17]  The Supreme Court reiterated the standard of review in an earlier opinion involving the same Batson challenge raised in Miller-El. Miller-El v. Cockrell, 537 U.S. 322, 340, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003) ("In the context of direct review, therefore, we have noted that the trial court's decision on the ultimate question of discriminatory intent represents a finding of fact of the sort accorded great deference on appeal and will not be overturned unless clearly erroneous.") (internal citations and quotes omitted).
[18]  Williams's sentencing judge was different from Davis's trial judge.
[19]  Davis argued this motion pro se with his back-up counsel present.
