
514 F.3d 193 (2008)
UNITED STATES of America, Appellant,
v.
Humberto PEPIN, Also Known as Homberto Pepin Taveras, Also Known as Tony, Humberto Pepin Taveras, Defendant-Appellee.
Docket Nos. 06-1462-cr(L), 06-2566-cr(con), 06-3284-cr(con).
United States Court of Appeals, Second Circuit.
Argued: September 6, 2007.
Decided: February 6, 2008.
*194 David L. Lewis (Louis M. Freeman, Freeman Nooter & Ginsberg, of counsel), New York, NY, for Defendant-Appellee.
Lee J. Freedman, Assistant United States Attorney for the Eastern District of New York (Roslynn R. Mauskopf, United States Attorney, Peter A. Norling, Assistant United States Attorney, of counsel), Brooklyn, NY, for Appellant.
Before: WALKER, CALABRESI, and SACK, Circuit Judges.
SACK, Circuit Judge:
*195 The defendant, Humberto Pepin,[1] awaits trial on (1) one count of obstruction of justice, and (2) two counts of murder committed while engaged in drug trafficking. The government seeks the death penalty as to the latter.
The government proffered as evidence supporting a "non-statutory aggravating factor" of "future dangerousness," Pepin's "engage[ment] in a continuing pattern of violence," including "child abuse," for the jury to consider at the penalty phase. Notice of Intent to Seek a Sentence of Death dated October 20, 2005, United States v. Taveras, No. 04-cr-156 (E.D.N.Y.), ("Notice"), at 4, 12. The district court (Jack B. Weinstein, Judge) granted a motion by Pepin to preclude such evidence at the penalty phase on grounds that such matters were unrelated to "future dangerousness" or the crimes charged in the indictment.
The government then sought to amend its Notice to include, as a separate nonstatutory aggravating factor, "moral condemnation," to be supported by the defendant's prior conviction for child endangerment and related behavior. The court concluded that "[s]ubstantively, the amendment cannot stand." United States v. Taveras, 436 F.Supp.2d 493, 502 (E.D.N.Y.2006). All evidence the government might adduce to support the proposed factor would therefore be excluded for essentially the reasons that the same evidence had been excluded as support for a "future dangerousness" factor.
Finally, after Pepin raised the issue of the admissibility of photographs of the victims' dismembered bodies, the district court, sua sponte, issued an order precluding all evidence as to dismemberment at either the guilt phase or the penalty phase of the trial.
We affirm as to the orders related to the admission of evidence of Pepin's alleged child abuse and of his child-endangerment conviction at the penalty phase, but vacate the order barring all evidence related to dismemberment at the guilt phase.

BACKGROUND
In a superseding indictment dated October 20, 2005, filed in the United States District Court for the Eastern District of New York,[2] Pepin was charged with, inter alia, (1) one count of obstruction of justice, in violation of 18 U.S.C. § 1512(b)(3), and (2) two counts of murder committed while Pepin was engaged in drug trafficking, in violation of 21 U.S.C. § 848(e)(1)(A).[3] If convicted on either or both of the latter two charges, Pepin is subject to a minimum sentence, under 21 U.S.C. § 848(e)(1)(A), of 20 years' imprisonment and a maximum penalty of death.[4] The government seeks the death penalty.
*196 Because this is a capital case, the Federal Death Penalty Act ("FDPA"), 18 U.S.C. § 3591 et seq., provides the procedures to be employed at sentencing. The district court is required by the FDPA, among other things, to "conduct a separate sentencing hearing to determine the punishment to be imposed." 18 U.S.C. § 3593(b). The hearing will ordinarily be held "before the jury that determined the defendant's guilt." 18 U.S.C. § 3593(b)(1).
[T]he jury . . . shall consider whether all the aggravating factor or factors found to exist sufficiently outweigh all the mitigating factor or factors found to exist to justify a sentence of death; or, in the absence of a mitigating factor, whether the aggravating factor or factors alone are sufficient to justify a sentence of death. Based upon this consideration, the jury by unanimous vote . . . shall recommend whether the defendant should be sentenced to death, to life imprisonment without possibility of release or some other lesser sentence.
18 U.S.C. § 3593(e).
Charged Murders and Post-Homicide Conduct
In support of the charges contained in the October 20, 2005, superseding indictment, the government states that it intends to prove "through witness testimony, Pepin's statements to law enforcement officers, photographs of his victims after they were recovered, and autopsy reports and photographs," Gov't Br. at 3, the following facts:
Pepin was born in the Dominican Republic. In or about 1981, he entered the United States illegally, eventually settling in New York City. At all relevant times, he sold drugs from an apartment in the Bronx which he rented for that purpose. See id.; Written Statement of Humberto Pepin Taver[a]s to Yonkers Police Detective Geiss dated October 15, 2002[5] (the "Pepin Statement") (stating that the apartment was on Sherman Avenue in the Bronx).
The Rosario Killing. José Rosario was one of Pepin's sources for drugs. The two of them had an arrangement under which Rosario robbed dealers of their drugs and then supplied those drugs to Pepin. Pepin then sold them, sharing the proceeds with Rosario. Gov't Br. at 4. In or about September 1992, a Pepin associate known as "Nelo" told Pepin that Rosario had instructed him, Nelo, to kill Pepin. Id.
On or about September 17, 2002, Rosario visited Pepin's Bronx apartment where Pepin, in the presence of George Loyola, one of Pepin's drug sellers, shot Rosario several times. Pepin then ordered Loyola at gunpoint to help Pepin carry Rosario's body into the bathroom. They placed the body in the bathtub and left the bathroom. Pepin returned shortly thereafter when he heard noises suggesting that Rosario might still be alive. Pepin cut Rosario's neck so that he would bleed to death and the blood would drain from the tub. Id.
Loyola and Pepin left the Bronx apartment. Pepin went home where his girlfriend, Julia Mendez, was waiting. Pepin told Mendez that he had killed Rosario. He then ordered her to make dinner for him. Afterward, Pepin forced Mendez to come with him to the Bronx apartment, stopping en route to purchase a knife. Id.
Pepin's cousin, Apolinar Taveras, and Loyola joined Pepin at the Bronx apartment. Unable to coerce Loyola to assist him, Pepin dismembered Rosario's body by himself, using the knife he had just purchased. He placed the body parts into garbage bags. Pepin then forced Loyola to accompany Pepin to Yonkers, where *197 Pepin dumped the bags. Rosario's remains were discovered soon thereafter.[6]Id. at 4-5.
The Madrid Killing. More than two years later, on October 4, 1994, Pepin was arrested by Federal Drug Enforcement Administration agents following a search of another apartment that Pepin was renting. The search resulted in the seizure of drugs and Pepin's indictment in the United States District Court for the Southern District of New York on federal drug charges. Pepin was released pending trial on a bond signed by Carlos Madrid, another Pepin associate, as a surety. Id. at 6.
Sometime thereafter, Pepin and Mendez went to Madrid's home in Queens, where Pepin asked Madrid for money. Madrid gave Pepin twenty dollars, far less than Pepin had sought. On the way home, Pepin's BMW struck a guardrail. Upset, Pepin told Mendez that Madrid was "going to have to pay." Id.
By October 1995, Mendez, by then separated from Pepin, had moved into her sister's residence. Pepin and Mendez were nonetheless attempting to reconcile. On or about October 9, 1995, Pepin picked Mendez up at her sister's home, saying that he wanted to take Mendez to dinner. Instead, he drove her to his house. Id.
When they arrived, Pepin ordered Mendez into the bedroom. He told her that he was waiting for Madrid because that day Madrid was "going to pay for what he did." Id. He told her to play video games with the television sound turned up. He then left the bedroom, locking Mendez inside. Id.
Pepin had asked Madrid to the house on the pretext that he, Pepin, wanted to buy drugs from Madrid. When Madrid arrived with the drugs, Pepin brought Madrid into the bedroom to say hello to Mendez. The two men then left the room. Id. at 7. Shortly thereafter, Mendez heard several loud noises. They were, it turned out, the sound of Pepin hitting Madrid over the head with a blunt instrument. Pepin also stabbed Madrid with a knife. The injuries Pepin inflicted on Madrid were fatal.
About fifteen minutes later, Pepin entered the, bedroom and told Mendez to buy garbage bags and cleaning supplies and to avert her eyes from the kitchen area as *198 she left. Mendez nonetheless looked into the kitchen as she passed and saw a pair of legs in a puddle of blood. On her return, the door leading to the kitchen was closed. Mendez returned to the bedroom. Id. at 7-8.
Pepin dismembered Madrid's body and placed the body parts in trash bags. Mendez later saw Pepin placing a bag in the trunk of Madrid's automobile. Id. at 8.
Pepin and Mendez left togetherPepin driving Madrid's car; Mendez driving Pepin's. Pepin dumped most of the bags containing the body parts, but at least onewith Madrid's severed head inside itwas left in the automobile, which Pepin unsuccessfully attempted to burn. Soon thereafter, authorities recovered the remains. Id.
Child Abuse Allegations
The government seeks to present evidence during the penalty phase of Pepin's trialif there is oneregarding Pepin's treatment of Mendez's children.
According to the government, Mendez moved in with Pepin in 1989, along with her son and daughter from a prior relationship. At the time, the girl was eight years old. Pepin confined the children to a single room of their apartment, made them use a bucket as a latrine, and frequently prevented Mendez from providing food to them. The government also contends that Pepin vaginally and anally raped Mendez's daughter on many occasions, beat her when she informed Pepin, truthfully, that she was pregnant, and carved his name into her chest using a needle. Id. at 9-10.
On January 2, 1997, the Bronx County District Attorney's office charged Pepin with rape, sodomy, assault, possession of a weapon, and endangering the welfare of a child. Pepin later pleaded guilty to a misdemeanor charge of endangering the welfare of a child in satisfaction of all charges against him. He served nine months in prison and was then deported to the Dominican Republic. Id. at 10.
Less than six months later, Pepin was arrested attempting to re-enter the United States. He was subsequently convicted on federal charges of illegal re-entry, bail jumping, and drug trafficking. Id. While in prison on those charges, he wrote a letter to a Yonkers police officer admitting that he had had sexual relations with Mendez's daughter but denying that he did so against her will. Id.[7] (citing letter, date obscure, from Pepin, in Otisville, to "Señor John Geiss.").
District Court Ruling as to Evidence of Child Abuse
On October 20, 2005, the government filed a superseding Notice of Intent to Seek a Sentence of Death, pursuant to 18 U.S.C. § 3593(a), in which "future dangerousness" was proffered as a "non-statutory aggravating factor" as follows:
The defendant HUMBERTO PEPIN TAVERAS is likely to commit criminal acts of violence in the future that would constitute a continuing and serious threat to the lives and safety of others, as evidenced by, at least, one or more of the following:
a. Continuing Pattern of Violence
The defendant HUMBERTO PEPIN TAVERAS has engaged in a continuing pattern of violence, attempted violence, and threatened violence, including, at least, (a) the crimes charged in the Indictment, (b) the crimes for which the defendant has been previously *199 convicted, (c) child abuse, (d) domestic abuse and (e) threatening and attempting to kill John Doe, a witness against the defendant.
Notice at 3-4, 11-12 (emphasis added).[8]
On February 28, 2006, the district court issued a Memorandum and Order that, inter alia, excluded at the penalty phase all evidence related to allegations of acts of violence and abuse against the child and the adult women set forth in the Notice as non-statutory aggravating factors. The court found the evidence to be unduly prejudicial under Federal Rule of Evidence 403. United States v. Taveras, 04-cr-156, 2006 WL 473773, at *6, 2006 U.S. Dist. LEXIS 7408, at *17-*18 (E.D.N.Y. Feb. 28, 2006) ("Memorandum and Order on Challenges to Death Penalty") ("Taveras I"). The court concluded:
[F]or Rule 403 reasons and others [previously] explained orally [by the court], evidence of the aggravating factors of sexual crimes committed on a minor and a sexual assault on an adult will not be permitted. They do not relate to the homicidal characteristics which form the basis of the prosecution and they might well be overvalued in light of recent publicity on sexual assaults on children in this geographic area.
Id., 2006 WL 473773, at *6, 2006 U.S. Dist. LEXIS 7408, at *17-*18.
On March 16, 2006, the court, relying on 21 U.S.C. § 848(j) (repealed),[9] revisited its decision excluding evidence of Pepin's violence against adult women and decided to allow it. But the court reaffirmed its decision to exclude evidence as to child abuse, which it explained in greater detail. United States v. Taveras, 424 F.Supp.2d 446 (E.D.N.Y.2006) ("Taveras II"). Noting that there was a "great likelihood that defendant, if convicted and spared death, will spend the rest of his life in prison," id. at 463, the court viewed evidence of sexual and physical abuse against minors as irrelevant to future dangerousness because of the unlikelihood of his release into the community, id. The court also concluded that admission of such evidence would confuse the jury, id., and, "[s]ince the government bears the burden of proving these charges beyond a reasonable doubt, proof would require a diversionary trial within a trial that would have minimal relevance to the future danger posed by defendant to those with whom he is, if convicted, likely to spend the rest of his lifeadult guards and male inmates," id. at 463-64. The court continued:
More importantly, the evidence would be likely to so inflame the passions of the jurors as to inhibit their careful consideration of the future dangerousness factor. Wide attention to a recent spate of sexual assaults against minors would make it almost impossible for a jury to disconnect its anger at the prevalence of the crimes from the issue of future dangerousness of this defendant. Defendant's contentions that the relationship was consensual would confuse the issues by directing the jury's energies towards divining the nature of the relationship between the two rather than the need to protect society from future crimes of defendant, the basis of the future dangerousness factor. Introduction of this evidence would not produce the heightened *200 reliability required of a capital sentence.
Id. at 464.
On or about March 23, 2006, the government, undaunted, sought to file another superseding Notice of Intent to Seek a Sentence of Death. Notice of Intent To Seek Sentence of Death dated March 22, 2006, United States v. Taveras, No. 04-CR-156 (E.D.N.Y.), accompanying motion for leave to file the amended Notice filed on March 23, 2006. This time, instead of adverting to child abuse as an indication of future dangerousness, the proposed superseding Notice set forth as a separate non-statutory aggravating factor Pepin's previous conviction for child endangerment and related behavior. Id. at 5-6. The proposed superseding Notice added the as sertion that "[b]eyond raping the child, the defendant repeatedly falsely imprisoned the child, deprived her of food and water, and beat her. On one occasion, the defendant carved his nickname, `Tony,' on the child's chest." Id. These facts, the proposed superseding Notice said, "demonstrate [] that the defendant merits moral condemnation by the community." Id. at 6.
On May 4, 2006, at a status conference, the district court invoked its discretion, not under 21 U.S.C. § 848(j) (repealed) as it had previously done, but under 18 U.S.C. § 3593(e), which governs admissibility of evidence at the penalty phase of capital trials. Section 3593(c) provides, in part, that "[i]nformation is admissible regardless of its admissibility under the rules governing admission of evidence at criminal trials except that information may be excluded if its probative value is outweighed by the danger of creating unfair prejudice, confusing the issues, or misleading the jury.[10] The court decided that "[the government's] amendment is permitted but [it will] be allowed no evidence on it." Hearing Transcript, May 4, 2006, at 29.
The court further explained its position in an "Omnibus Pretrial Memorandum and Order" dated June 29, 2006. United States v. Taveras, 436 F.Supp.2d 493 (E.D.N.Y.2006) ("Taveras III"). "The new proposed notice would not add new allegations, but merely reorganize them in response to this court's ruling" excluding evidence as to child abuse. Id. at 502. Although the motion to amend was procedurally "unobjectionable" because the government's application was made in good faith and Pepin was not prejudiced by it, id., "[s]ubstantively, the amendment cannot stand. Nothing in the government's motion justifies [the court's] departure from [its] previous ruling excluding this same evidence. See [Taveras II], 424 F.Supp.2d at 463-64. The more stringent standard of admissibility provided for by title 18's FDPA strengthens the basis for the ruling that this evidence is inadmissible." Taveras III, 436 F.Supp.2d at 502-03.[11]
*201 District Court Ruling as to Evidence of Post-Mortem Dismemberment
In Taveras III, the district court also excluded all evidence of, post-mortem dismemberment of the victims in both the guilt and penalty phases of trial. The court indicated that if one looked at the guilt phase alone, the dismemberment evidence would be permitted. "These details form part of the res gestae, the narrative that the government rightly seeks to tell at the guilt phase of a trial. Old Chief v. United States, 519 U.S. 172, 187, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997). Their probative value would not be `substantially outweighed by the danger of unfair prejudice. . . .' Fed.R.Evid. 403." Id. at 514. But, the court ruled, any such evidence was inadmissible in the penalty phase because it would "short-circuit" the process "carefully choreographed" by section 3593 for determining the appropriate sentence "by tending to rush the jury into an emotional conclusion." Id. at 515.
"It is of vital importance to the defendant and to the community that any decision to impose the death sentence be, and appear to be, based on reason rather than caprice or emotion." Gardner v. Florida, 430 U.S. 349, 358, 97 S.Ct. 1197, 51 L.Ed.2d 393 (1977). The court has a duty to minimize the "risk [of] a verdict impermissibly based on passion, not deliberation." Payne v. Tennessee, 501 U.S. 808, 836, 111 S.Ct. 2597, 115 L.Ed.2d 720 (1991) (Souter, J., concurring).
Id. (brackets in original).
The court then decided that despite its conclusion that the dismemberment evidence would have been allowed under Federal Rule of Evidence 403 if the court's concern was solely whether its probative value was substantially outweighed by the danger of unfair prejudice at the guilt phase of the trial, the need to exclude the evidence at the penalty phase required its exclusion at the guilt phase, too. "Since one jury will hear both the penalty and guilt phases, such evidence also will not be received at the guilt phase." Id. at 515-16.
Instead, the court said, it "expected" the parties to "stipulate that: After killing Rosario, defendant returned home, ate dinner, and then returned to the apartment with Julia Mendez. Defendant wrapped the body, drove it to Yonkers with Loyola, and dumped it. After killing Madrid, defendant wrapped the body, placed it in Madrid's car, drove the car to Queens, and set it on fire." Id. at 516. "This ruling sacrifices some of the probative force of the government's proposed evidence. Yet it is necessary to preserve defendant's right to capital proceedings that are properly channeled and focused on the issue for which the evidence is offeredi.e., future dangerousness." Id. Reference to dismemberment during voir dire was also prohibited. Id.
The government appeals from the orders excluding evidence of child abuse or evidence related to the child endangerment conviction, from the penalty phase, and the order excluding post-mortem dismemberment evidence from both the guilt and penalty phases of trial. On September 6, 2007, we granted the government's motion for a stay of the trial pending our resolution of this appeal.

DISCUSSION
I. Jurisdiction
We have jurisdiction to consider this appeal under 18 U.S.C. § 3731. See, e.g., United States v. Chevere, 368 F.3d 120 (2d Cir.2004) (hearing government's challenge to pre-trial evidentiary ruling on interlocutory *202 appeal).[12]
II. Standard of Review
"[W]e review evidentiary rulings for abuse of discretion." United States v. Sewell, 252 F.3d 647, 650 (2d Cir.), cert. denied, 534 U.S. 968, 122 S.Ct. 382, 151 L.Ed.2d 291 (2001); see also Awadallah, 436 F.3d at 131 ("We review the exclusion of evidence pursuant to Rule[ 403 . . . for abuse of discretion."); United States v. Salameh, 152 F.3d 88, 110 (2d Cir.1998) (per curiam) (concluding that Fed.R.Evid. 403 determinations may be overturned "`only if there is a clear showing that the court abused its discretion or acted arbitrarily or irrationally'" (quoting United States v. Valdez, 16 F.3d 1324, 1332 (2d Cir.1994))), cert. denied sub nom. Abouhalima v. United States, 525 U.S. 1112, 119 S.Ct. 885, 142 L.Ed.2d 785 (1999).
Although we have not squarely addressed the question before, we see no reason to apply a different standard of review to a district court's ruling that information proffered by the government as evidence is inadmissible at the penalty phase of a capital prosecution under section 3593(c). The other circuit courts to reach this issue have taken a similar approach, deciding that, absent constitutional or other legal errors, a district court's section 3593(c) rulings are reviewed for abuse of discretion. See United States v. Hall, 152 F.3d 381, 397-98 (5th Cir.1998) ("[T]he district court has considerable discretion in controlling the presentation of the `information' to the jury in both content and form." (internal quotations omitted)); United States v. McVeigh, 153 F.3d 1166, 1214 (10th Cir.1998) ("We review a district court's determination that evidence is not relevant to a mitigating factor for abuse of discretion."); United States v. Johnson, 223 F.3d 665, 674 (7th Cir.2000) ("The [section 3593(c)] balancing is committed to the discretion of the district judge, not here abused." (citing Hall, 152 F.3d at 397)).
Our review must, however, "be de novo on the question whether, in exercising its discretion to admit evidence, the district court applied the proper legal test." Borawick v. Shay, 68 F.3d 597, 601 (2d Cir. 1995) (citing A/S Dampskibsselskabet Torm v. Beaumont Oil Ltd., 927 F.2d 713, 716 (2d Cir.1991)), cert. denied, 517 U.S. 1229, 116 S.Ct. 1869, 134 L.Ed.2d 966 (1996).
The government is understandably wary of our reviewing the district court's rulings under the deferential abuse of discretion standard. It therefore attempts to phrase its arguments as challenges to the legal bases for the district court's rulings, which we would review de novo. The government does not so much as mention the *203 abuse of discretion standard until the second footnote of its reply brief. We nonetheless review the court's orders both for errors of law and abuse of discretion.[13]
III. The Exclusion of Evidence of Child Abuse and the Child Endangerment Conviction
A. Errors of Law
18 U.S.C. § 3593(c) provides, in pertinent part:
Proof of mitigating and aggravating factors. . . .  At the sentencing hearing, information may be presented as to any matter relevant to the sentence, including any mitigating or aggravating factor permitted or required to be considered under section 3592. Information presented may include the trial transcript and exhibits if the hearing is held before a jury or judge not present during the trial, or at the trial judge's discretion. The defendant may present any information relevant to a mitigating factor. The government may present any information relevant to an aggravating factor for which notice has been provided [by a notice to seek the death penalty]. Information is admissible regardless of its admissibility under the, rules governing admission of evidence at criminal trials except that information may be excluded if its probative value is outweighed by the danger of creating unfair prejudice, confusing the issues, or misleading the jury. . . . The government and the defendant shall be permitted to rebut any information received at the hearing, and shall be given fair opportunity to present argument as to the adequacy of the information to establish the existence of any aggravating or mitigating factor, and as to the appropriateness in the case of imposing a sentence of death. . . . The burden of establishing the existence of any aggravating factor is on the government, and is not satisfied unless the existence of such a factor is established beyond a reasonable doubt. The burden of establishing the existence of any mitigating factor is on the defendant, and is not satisfied unless the existence of such a factor is established by a preponderance of the information.
Id. Section 3593(c) therefore provides the legal standard upon which the district court could exclude what it deemed to be unduly prejudicial evidence at the penalty phase of trial. See United States v. Fell, 360 F.3d 135, 140-41 (2d Cir.), cert. denied, 543 U.S. 946, 125 S.Ct. 369, 160 L.Ed.2d 259 (2004).[14] The gravamen of the government's *204 legal argument is that despite the statute's instruction that "information may be excluded if its probative value is outweighed by the danger of creating unfair prejudice, confusing the issues, or misleading the jury," section 3593(c) as a whole mandates the district court's admission, in the penalty phase of this case, of evidence as to child abuse or the child endangerment conviction, or both. We conclude that it does not.
It is true, as the government points out, Gov't Br. at 31, that in United States v. Fell, we noted, "the Supreme Court has . . . made [it] clear that in order to achieve [the required] `heightened reliability[]' [in the penalty phase of a capital case], more evidence, not less, should be admitted on the presence or absence of aggravating and mitigating factors." Fell, 360 F.3d at 143 (citing Gregg v. Georgia, 428 U.S. 153, 203-04, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976)). But it hardly follows from that general observation that relevant evidence is always permitted. Acceptance of that reasoning would eviscerate the trial court's ability to exclude unduly prejudicial material from the penalty hearing inasmuch as any decision to exclude necessarily means less evidence, not more.
In upholding the constitutionality of section 3593(c) in Fell, we noted that the requirement of a fundamentally fair trial
is certainly met [by section 3593(c)], given that the balancing test set forth in the FDPA is, in fact, more stringent than its counterpart in the [Federal Rules of Evidence], which allows the exclusion of relevant evidence "if its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury." Fed.R.Evid. 403 . . . Thus, the presumption of admissibility of relevant evidence is actually narrower under the FDPA than under the FRE.
Fell, 360 F.3d at 145 (first emphasis added). We then pointed out that:
The FDPA does not eliminate [the] function of the judge as gatekeeper of constitutionally permissible evidence; nor does it alter or eliminate the constitutional baseline for the admissibility of evidence in a criminal trial. To the contrary, under the FDPA [s]tandard, judges continue their role as evidentiary gatekeepers and, pursuant to the balancing test set forth in § 3593(c), retain the discretion to exclude any type of unreliable or prejudicial evidence that might render a trial fundamentally unfair.
Id. (citations, internal quotation marks, and brackets omitted). Fell does not support the government's contention.
Citing Gregg v. Georgia, supra, and Williams v. New York, 337 U.S. 241, 69 S.Ct. 1079, 93 L.Ed. 1337 (1949), the government also insists that "to be constitutional, a capital sentencing procedure must be individualized and based on the fullest possible information about the defendant" Gov't Br. at 33. But Gregg did not hold that the government is entitled to present to the jury "the fullest possible information about the defendant" regardless of what that information might be. It concluded that a Georgia capital trial scheme much like the FDPA was constitutional, in part because it "provides for a bifurcated proceeding at which the sentencing authority is apprised of the information relevant to the imposition of sentence and provided with standards to guide its use of the information." Gregg, 428 U.S. at 195, 96 S.Ct. 2909. The proceedings before us *205 meet that standard, whatever the district court's ruling was on the admissibility of evidence of child abuse. Similarly, the Williams Court approved a sentencing judge's ability, in determining that a death sentence was warranted, to consider evidence of other crimes of which the defendant had not been convicted but in which he had been implicated. Williams, 337 U.S. at 244, 69 S.Ct. 1079.[15] The ability of the court to admit such evidence at the penalty phase is not at issue here. While both Gregg and Williams might be read to suggest that the district court was permitted to admit evidence related to child abuse and the conviction for child endangerment consistent with the requirements of due process, they plainly do not require the district court to do so as a matter of law.
The other arguments the government makes on this score are of a similar stripe. For example, the government tells us that the Ninth Circuit "upheld a sentencing jury's consideration of the defendant's lewd and lascivious conduct conviction . . . and his unadjudicated rape of an adult." Gov't Br. at 36 (citing McDowell v. Calderon, 107 F.3d 1351, 1366, amended and superseded in part by 116 F.3d 364, vacated in part, 130 F.3d 833 (9th Cir.1997) (en banc), cert. denied, 523 U.S. 1103, 118 S.Ct. 1575, 140 L.Ed.2d 807 (1998)). And, it asserts, "[o]ther courts have admitted information about prior violent acts such as rape, assault and child abuse to inform the jury's decision regarding future dangerousness." Gov't Br. at 38 (citing McDowell, 107 F.3d at 1366;. Hogue v. Scott, 874 F.Supp. 1486, 1509-11, 1524 (N.D.Tex.1994), aff'd, 131 F.3d 466 (5th Cir.1997), cert. denied, 523 U.S. 1014, 118 S.Ct. 1297, 140 L.Ed.2d 334 (1998)). That may be so. But it does not follow that the district court in this case and on this record was required by law to rule that the prejudicial effect of the evidence in question did not outweigh its probative value.
There was no error of law.
B. Abuse of Discretion
When reviewing the exercise of a district court's discretion in the context of admissibility of evidence under Federal Rule of Evidence 403, we will not disturb the court's conclusion "so long as [it] has conscientiously balanced the proffered evidence's probative value with the risk for prejudice," and our intervention is limited only to those cases where the court's decision is "arbitrary or irrational." Awadallah, 436 F.3d at 131 (citing United States v. Han, 230 F.3d 560, 564 (2d Cir.2000)); see also id. (quoting Hester v. BIC Corp., 225 F.3d 178, 181 (2d Cir.2000) ("A district court's evidentiary rulings will be disturbed only if they are `manifestly erroneous.'" (quoting Luciano v. Olsten Corp., 110 F.3d 210, 217 (2d Cir.1997)))). We
*206 In the case before us, the district court explained at different times, and in some detail, its decision to exclude evidence as to child abuse and the prior child endangerment conviction. According to the court: "[This evidence does] not relate to the homicidal characteristics which form the basis of the prosecution," Taveras I, 2006 WL 473773, at *6, 2006 U.S. Dist. LEXIS 7408, at *18; it "might well be overvalued in light of recent publicity on sexual assaults on children in this geographic area," id., 2006 WL 473773, at *6, 2006 U.S. Dist. LEXIS 7408, at *18; there is a "great likelihood that defendant, if convicted and spared death, will spend the rest of his life in prison" and therefore his dangerousness to minor children and women is of little relevance, Taveras II, 424 F.Supp.2d at 463; it is possible that admission of the evidence would necessitate a "diversionary trial within a trial" as to whether Pepin's sexual relationship with Mendez's daughter was consensual and whether he abused her, id. at 463-64; it is likely that the evidence would "so inflame the passions of the jurors as to inhibit their careful consideration of the future dangerousness factor," id. at 464. When the government amended its Notice of Intent to Seek a Sentence of Death to add the child endangerment conviction as a means of putting much the same evidence before the jury under the rubric of "moral condemnation," the court further observed that it had earlier failed to have admitted as evidence of "future dangerousness," and that "[n]othing in the government's motion justifies departure from the court's previous ruling excluding this same evidence," Taveras III, 436 F.Supp.2d at 502-03. The district court thus made "a `conscientious assessment' of whether unfair prejudice substantially outweighs probative value." Salameh, 152 F.3d at 110 (quoting United States v. Birney, 686 F.2d 102, 106 (2d Cir.1982)). We cannot conclude that its analysis bespeaks an "arbitrary or irrational" exercise of discretion, Awadallah, 436 F.3d at 131, or results in an evidentiary ruling that is "manifestly erroneous," Hester, 225 F.3d at 181. We therefore affirm as to these orders.
We pause to note that this evidentiary challenge is unusual because it is made, properly under 18 U.S.C. § 3731, by way of pre-trial interlocutory appeal rather than being brought post-trial, post-verdict, and post-judgment. Nonetheless, the fair and proper conduct of a trial must be, and is, primarily in the hands of the trial judge. The standard of review, whether before trial or after, is, therefore, abuse of discretion. See, e.g., Awadallah, 436 F.3d at 131 (applying abuse of discretion review in a pre-trial appeal by the government to a district court's evidentiary ruling pursuant to 18 U.S.C. § 3731). Even were we to disagree with its conclusion as to the admissibility of child abuse evidence, then, we would not simply substitute our judgment for that of the district court.
IV. The Exclusion of Evidence of Post-Mortem Dismemberment
The government's challenge to the exclusion from both the guilt and penalty phases of all evidence regarding the victims' post-mortem dismemberment raises somewhat different issues.
The parties offer different accounts of the reasoning behind the district court's decision to exclude the dismemberment evidence from the guilt phase of the trial. The government argues, in essence, that the district court found the evidence admissible under Rule 403, but went on to exclude it nonetheless, because the evidence was not independently admissible during the penalty phase. The defense contends that the district court based its ruling on Rule 403 alone, which permits a *207 judge to consider both the defendant's willingness to stipulate and the potential for prejudice in the penalty phase in conducting the requisite balancing. Thus, under the government's view, we would review the decision de novo as a question of law, while under the defendant's view, we would only ask whether the application of Rule 403 constituted an abuse of discretion. While both are reasonable characterizations of the district court's order in Taveras III, we find it unnecessary to choose between them. Whether the district court applied a novel rule of law or relied on Rule 403, we conclude that its order with respect to the dismemberment evidence at the guilt phase must be vacated.
A. Errors of Law
First, as the district court acknowledged, Federal Rule of Evidence 403, providing that "evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice. . . ." (emphasis added), governs admissibility of evidence at the guilt phase. Taveras III, 436 F.Supp.2d at 513. As we have noted, a district court ordinarily has somewhat less latitude to exclude probative evidence based on unfair prejudice at the guilt phase, under Rule 403, than it does where the evidence is offered only at the penalty phase and where the court's exercise of discretion is, therefore, governed by the more stringent evidentiary standard of 18 U.S.C. § 3593(c). Inasmuch as the question before us is the admissibility of dismemberment evidence at the guilt phase, it would appear that Rule 403 applies here. If so, the district court can exclude such evidence only if the danger of unfair prejudice "substantially outweighs" its probative value under Rule 403, not if the one merely "outweighs" the other as section 3593(c) 19 permits.
According to the government, the district court excluded the evidence at the guilt phase, even after finding it admissible under Rule 403, because it was not independently admissible during a potential penalty phase. This decision, it argues, is both contrary to section 3593(c) and unsupported by any authority.
As the district court was keenly aware, a court has two separate sets of responsibilities with respect to evidence that a single jury may consider twice, once when deciding between guilt and acquittal, the other when deciding between life and death. Insofar as the district court fashioned a novel rule governing evidence at the guilt phase of a capital trial, it was clearly attempting to meet both responsibilities rather than one at the expense of the other. Nevertheless, if and to the extent that the district court excluded evidence from the guilt phase solely because it was excluded at the penalty phase, we conclude that it erred as a matter of law.
We do not think that the district court, in making its Rule 403 determinations, is required to ignore its subsequent obligation to apply the section 3593(c) standard at the penalty phase. To rule that only evidence independently admissible at the penalty phase is admissible during the guilt phase, however, would impermissibly allow the section 3593(c) admissibility standard to govern evidentiary rulings not only at the penalty phase, but throughout the entire proceeding.
B. Abuse of Discretion
Although acknowledging once again the degree of deference we pay to a district court's ruling on the admissibility of evidence, we also conclude that the order excluding all evidence as to post-mortem dismemberment, to the extent that it relies on Rule 403, was an abuse of discretion.
*208 The issue at the guilt phase will be whether the killings of Rosario and Madrid by Pepin were "intentional." See Taveras III, 436 F.Supp.2d at 514. The importance of dismemberment evidence to the prosecution was cogently stated by the district court:
[A]spects of the photographs and testimonyparticularly the precise manner in which the bodies were dismemberedare . . . highly probative of [the] mental state [in issue].
At the guilt phase, such evidence would be pertinent. To secure a conviction on the capital charges, the prosecution must convince the jury beyond a reasonable doubt that defendant "intentionally kill[ed] or counsel[led], command[ed], induce[d], procure[d], or cause[d] the intentional killing of an individual and such killing result[ed]." 21 U.S.C. § 848(e)(1)(A). Defendant has indicated that he does not intend to contest that he killed Madrid and Rosario, lessening the need for witness testimony on the fact of the killing. A stipulation to the victims' deaths at defendant's hands would thus be an alternative source of proof. See Old Chief v. United States, 519 U.S. [172,] 184 [117 S.Ct. 644, 136 L.Ed.2d 574] [(1997)] ("[T]he Rule 403 `probative value' of an item of evidence . . . may be calculated by comparing evidentiary alternatives."). Yet the government must prove not merely the fact of the killing, but defendant's intent. Evidence that defendant calmly dismembered the victims' bodies shortly after killing them would tend to show that the killings were not accidentalthat is, that he was calm, collected, and rational shortly before the killings. The precise manner in which defendant disposed of the bodiesusing a knife and drawing on his skill as a butcher to cut at the jointssuggests not a panicked reaction to accidental death but a considered effort to hide a criminal act. These details form part of the res gestae, the narrative that the government rightly seeks to tell at the guilt phase of a trial. Old Chief v. United States, 519 U.S. [at] 187 [117 S.Ct. 644] . . . (1997). Their probative value would not be "substantially outweighed by the danger of unfair prejudice. . . ." Fed.R.Evid. 403.
Id. (some brackets added).
Even after factoring in the potential for unfair prejudice at the penalty phase, we conclude that in light of its importance in the context of the case as a wholeits "res gestae," as the district court termed it, id.the fact that Pepin dismembered the bodies of the deceased is potentially too important a factor in the jury's determination as to Pepin's guilt vel non of the crimes of which he is accused for it to be excluded altogether at the guilt phase. We assume without deciding that the evidence may later be excludable and therefore excluded under section 3593(c) during the penalty phase of the trial conducted before the same jury, and that the jury would thus have had access to information that should not be before it for purpose of evaluating the sentence to be imposed. But it would be odd, indeed, if the very gruesomeness of the killings of which Pepin has been charged were to disjoint and abbreviate the prosecution's presentation of the case against him, thus disadvantaging the government in its ability to establish to the jury beyond a reasonable doubt that Pepin committed an intentional homicide in the first place. The importance of the dismemberment evidence to the proper prosecution of the case, combined with the possibility of curative instructions at the penalty phase, if necessary, convince us that evidence of the dismemberments and their context must be allowed at the guilt phase.
*209 We do not mean to suggest that all evidence of dismemberment must be admitted at the guilt phase. But the blanket ban of dismemberment evidence from the guilt phase was an abuse of discretion, and we therefore vacate the order of the district court effecting such a ban.
The government also asks us to decide that evidence of dismemberment must be permitted at the penalty phase. We decline to do so. Much will have happened between now and then, particularly the likely use of evidence of dismemberment at the guilt phase. We cannot know with anything approaching certainty what the precise issue before the court will be if and when it actually is framed. We therefore vacate the order now in force barring dismemberment evidence from the penalty phase. Should these proceedings enter a penalty phase, we leave it to the district court at that timein light of the views expressed in this opinion and in the district court's sound discretionto enter an order as to the admissibility of such evidence.

CONCLUSION
For the foregoing reasons, the orders of the district court are affirmed, except its order with respect to evidence of dismemberment at the guilt and penalty phases of trial, which is vacated. The order of this Court staying the trial is vacated effective upon issuance of the mandate. Each party shall bear his or its own costs.
NOTES
[1]  The defendant has been referred to in and by the district court as Humberto Pepin Taveras. See, e.g., United States v. Taveras, 436 F.Supp.2d 493 (E.D.N.Y.2006). On appeal, though, he is referred to as Humberto Pepin, We therefore use the latter name.
[2]  Pepin was first indicted in the Eastern District on February 20, 2004.
[3]  The superseding indictment also charged Pepin with a firearm-related murder under 18 U.S.C. § 924(j)(1), but the district court granted Pepin's motion to dismiss that charge. The dismissal is not before us.
[4]  That statute provides in part:

any person engaging in . . . an offense punishable under section 841(b)(1)(A) of this title . . . who intentionally kills or counsels, commands, induces, procures, or causes the intentional killing of an individual and such killing results, shall be sentenced to any term of imprisonment, which shall not be less than 20 years, and which may be up to life imprisonment, or may be sentenced to death.
21 U.S.C. § 848(e)(1)(A).
[5]  In the statement, Pepin says that Yonkers Detective Wilson Gonsalez was also present.
[6]  On October 15, 1992, Pepin, incarcerated in the Otisville [N.Y.] Federal Correctional Facility, gave this version of the events to at least one Yonkers, New York, detective:

I walked into the bedroom, when I came out of the bedroom I had a 22 cal pistol. . . . [Rosario] was still seating [sic] on the couch. . . . I told him I was going to kill him. [Rosario] started to rise up off of the couch, I then pointed the gun at him and I shot him, I think 4 times, one was in the right eye I think, one wag in the neck, one in the chest, and I am not sure where the other shot went. . . . [M]yself and George [Loyola] dragged [Rosario] into the bathroom and put him in the tub. I put a cut into his neck so the blood would drain out. I then left to go to my house. . . . When I got home I ate and I told. . . . Julia [Mendez] that I killed [Rosario] and that I had to go back and cut up his body. . . . Julia asked me if I needed any help. I told her that I did. I then left with [her]. . . . I bought a large knife in the hardware store which is on Sherman Ave. . . . When I got to the apartment George [Loyola] asked me if my cousin Apolinar Taver[a]s could help us. I, told him yes and for him to get him. . . . A short time later we all cut up [Rosario] who was in the tub. I know how to cut up a body because in my country I worked as a butcher. I cut [Rosario] up by the joints, I cut off his head at the neck, I cut off his arm at the shoulder, his torso, his legs, his knees. I cut him up at the joints. We then placed him into separate garbage bags, I believe it was around 4 PM [M]yself and George [Loyola] and Apolinar came back when it was dark[,] . . . drove to Yonkers and I dumped the garbage bags in a park.
Pepin Statement at 1-2.
[7]  The letter is in Spanish. The record contains copies of the original and an English translation.
[8]  Prior versions of the Notice contained the same text.
[9]  21 U.S.C. § 848(j) provided, in pertinent part:

[I]nformation may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury.
Id.
[10]  By contrast, Federal Rule of Evidence 403, which applies during the guilt phase, provides: "Although relevant, evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury, or by considerations of undue delay, waste of time, or needless presentation of cumulative evidence." Id. (emphasis added). The analogous language in 18 U.S.C. § 3593(c) omits the word "substantially."
[11]  Although not entirely clear to us, it appears that the court was not denying the motion to file the amended notice. It was adhering to its earlier oral decision to permit the amendment to the Notice of Intent to Seek a Sentence of Death, but ordering all evidence as to the child endangerment conviction excluded. See Hearing Transcript, May 4, 2006, at 29. The precise characterization of the order in this regard does not, however, affect our consideration of this appeal.
[12]  18 U.S.C. § 3731 provides in pertinent part:

An appeal by the United States shall lie to a court of appeals from a decision or order of a district court suppressing or excluding evidence in a criminal proceeding, not made after the defendant has been put in jeopardy and before the verdict or finding on an indictment or information, if the United States attorney certifies to the district court that the appeal is not taken for purpose of delay and that the evidence is a substantial proof of a fact material in the proceeding.
This statute permits the government, under certain circumstances, to mount a pre-trial appellate challenge to a district court's decision rejecting trial evidence proffered by the government. But for the statute, in the event of an acquittal, the government would have no post-trial remedy for an erroneous evidentiary ruling, however serious the error, because of the operation of the Fifth Amendment's double-jeopardy bar. See United States v. Wilson, 420 U.S. 332, 335-40, 95 S.Ct. 1013, 43 L.Ed.2d 232 (1975).
[13]  We ordinarily adhere to the rule that "[i]ssues not sufficiently argued in the, briefs are considered waived and normally will not be addressed on appeal." Norton v. Sam's Club, 145 F.3d 114, 117 (2d Cir.), cert. denied, 525 U.S. 1001, 119 S.Ct. 511, 142 L.Ed.2d 424 (1998). And "[w]e generally do not consider issues raised in a reply brief for the first time because if an appellant raises a new argument in a reply brief an appellee may not have an adequate opportunity to respond to it." In re Harris, 464 F.3d 263, 268-69 n. 3 (2d Cir. 2006) (internal quotation marks and citations omitted). But we think that, in this case, the issues we address were indeed raised by the government, even though it asserted what was, in large measure, the wrong standard of review. There is no doubt, moreover, that the defendant had an opportunity to respond. His first words to us on this subject are: "The standard governing appellate review of the [district] court's evidentiary rulings is `abuse of discretion.'" Def.-Appellee Br, at 18.
[14]  In several instances, the district court does not appear to apply § 3593(c) in its analysis, instead discussing evidence in light of 21 U.S.C. § 848(j), now repealed. However, § 848(j)'s language utilized the less stringent "substantially outweighed" wording similar to that in Fed.R.Evid. 403. Because the test in section 3593(c) gives the court greater power to exclude prejudicial evidence than does the test in section 848(j) or Rule 403, the district court's conclusion would not likely have been different had it applied section 3593(c) from the outset, as the court acknowledges. See Taveras III, 436 F.Supp.2d at 500-01.
[15]  The Court stated:

A sentencing judge is not confined to the narrow issue of guilt. His task within fixed statutory or, constitutional limits is to determine the type and extent of punishment after the issue of guilt has been determined. Highly relevantif not essential to his selection of an appropriate sentence is the possession of the fullest information perceive no reason why the same degree of deference does not apply when a district court has excluded government-proffered evidence under 18 U.S.C. § 3593(b) in the penalty phase of a capital trial. possible concerning the defendant's life and characteristics. And modern concepts individualizing punishment have made it all the more necessary that a sentencing judge not be denied an opportunity to obtain pertinent information by a requirement of rigid adherence to restrictive rules of evidence properly applicable to the trial.
Williams, 337 U.S. at 247, 69 S.Ct. 1079.
