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Affirmed by published opinion. Judge NIEMEYER wrote an opinion, Parts I, IV and XVI of which Judge DIANA GRIBBON MOTZ and Judge KING joined. Judge DIANA GRIBBON MOTZ and Judge KING wrote a separate opinion that constitutes the court’s opinion on Parts II and III. OPINION NIEMEYER, Circuit Judge, writing for the court in Parts I, IV-XVI: A federal jury convicted Richard Allen Jackson of using a firearm during and in relation to kidnapping, sexually abusing, and murdering Karen Styles on October 31, 1994, in the Pisgah National Forest near Asheville, North Carolina, in violation of 18 U.S.C. § 924(j). Acting under the process required by 18 U.S.C. § 3593(e), the jury recommended that Jackson be sentenced to death. In accordance with that recommendation, the district court imposed the sentence of death on May 14, 2001. On appeal, Jackson contends: (1) that the district court erred in denying his motion to dismiss the indictment for prosecu-torial vindictiveness in light of the circumstances surrounding his State and federal prosecutions; (2) that the district court erred in denying his motion to dismiss on double-jeopardy grounds because he had been tried on the same facts in State court; (3) that the district court unconstitutionally excluded a juror on the basis of his death penalty views; (4) that the district court erred in denying Jackson’s motion for a mistrial based upon the alleged prosecutorial misconduct of calling a witness whose testimony was tainted and unreliable; (5) that the district court erred in admitting the testimony of stungun expert Dr. Robert Stratbucker; (6) that the district court erred in admitting the prior-act testimony of Georgia Katz and Maurice Evans, in violation of Federal Rule of Evidence 404(b); (7) that the district court unconstitutionally excluded evidence regarding the psychological and emotional condition of Jackson’s biological sister, proffered as mitigating evidence during the sentencing phase; (8) that the district court erroneously admitted, during the sentencing phase, an October 2000 videotaped interview of Jackson in rebuttal of the mitigating evidence presented by his mother, Sally Jackson; (9) that Jackson received ineffective assistance of counsel when one of his lawyers stated in his closing argument that “justice in this case says death”; (10) that the district court erred in allowing the jury to consider multiple intent factors when only one was necessary for imposition of the death penalty; (11) that the statutory aggravating circumstance found by the jury of “substantial planning and premeditation” is unconstitutionally vague; (12) that the district court erroneously instructed the jury when it failed to require that the entire jury consider a mitigating factor established if one juror found that factor to be established; (13) that the indictment was defective under the Fifth Amendment Indictment Clause, as interpreted in light of Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), and Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), for failing to allege aggravating circumstances necessary for the imposition of the death penalty, and that absent such allegations, the death penalty could not have been imposed; and (14) that the district court erred in denying Jackson’s motion to be returned to State custody to finish his preexisting State sentence before beginning his federal sentence, i.e., before being subject to the federal sentence of death. Upon review of the entire record and after consideration of all of the issues raised by Jackson on appeal, as well as whether the sentence of death was imposed under the influence of passion, prejudice, or any other arbitrary factor and whether the evidence supports the jury’s special finding of the existence of an aggravating factor required to be considered under 18 U.S.C. § 3592, we find no reversible error. See 18 U.S.C. § 3595. We state our reasons for the disposition of each of Jackson’s arguments in the opinions that follow. Parts I, IV-XVI of this opinion and Parts II and III as written in the separate opinion by Judge Motz and Judge King constitute the opinions of the court. Accordingly, we affirm Jackson’s conviction and the sentence of death imposed by the district court. I On Halloween morning, October 31, 1994, Karen Styles, a recent college graduate, disappeared from a trail in the Pisgah National Forest. A search initiated that evening, after Styles failed to return home, revealed no trace of Styles herself. Her car was, however, still parked at the lot at the head of the trail, and her car key was found on the trail two-tenths of a mile from the parking lot. A little more than three weeks later, Styles’ nude body was discovered by a hunter, duct-taped to a tree, where investigators also found a duct-tape wrapper, a pornographic magazine, and one spent Remington .22 caliber rifle casing. An autopsy revealed that Styles died from a single bullet wound to the head. She also had suffered ten stun-gun wounds to her body, nine of them inflicted within six inches of her pubic area. Investigators recognized from the duct-tape wrapper that the brand was sold at K-Mart. When sheriffs deputies contacted the nearest K-Mart store, located approximately one mile from the murder site, they discovered a receipt for a transaction that occurred on October 28, 1994, evidencing the purchase of a .22 rifle, a box of Remington .22 rifle ammunition, duct tape, a flashlight, and batteries. The ATF Form 4473 generated upon the purchase of the rifle revealed the purchaser to be Richard Allen Jackson. On December 20, 1994, Jackson voluntarily accompanied police to the Buncombe County Sheriffs Department for an interview. After the officers advised Jackson of his Miranda rights, Jackson waived them and answered questions for approximately three hours about his background and his whereabouts in the days surrounding the date of Styles’ murder. When the sheriff asked Jackson what he did with the rifle that he used to shoot Karen Styles, Jackson responded, “I think I need a lawyer present.” The sheriff then informed Jackson that he would not ask him any more questions and stated, “Son, I know you bought the rifle and the duct tape at K-Mart on the 28th of October. I know you were in Bent Creek on the day she was killed, and that’s fine, but you need help.” At this point Jackson broke down, crying and insisting that he did not mean to kill anybody. After the officers informed Jackson that he did not need to say anything because he had invoked his right to counsel, Jackson stated that he wanted to tell the whole story to get it off of his chest. He then signed another waiver of his Miranda rights. Jackson confessed fully. He stated that he arrived at the park around 8:00 a.m. and watched Styles as she stretched and walked down the trail. After sitting for a while, he took the gun out of the back of the car, loaded it, and started down the trail. He also had duct tape, a stun gun,- and a pornographic magazine in his coat pockets. After Karen Styles passed him on the trail, Jackson turned around and pointed the gun at her, whereupon Styles took a key out of her shoe and told Jackson that there was money in her car and that he could take the car. She pleaded with him not to hurt her. Jackson placed duct tape over Styles’ eyes and mouth and led her to a remote area, where he stood her with her back to a tree and duct-taped her to the tree. The duct tape on Styles’ mouth had come loose by this time, and Styles again asked him not to hurt her. Jackson taped her mouth shut again, ripped off her shorts and underpants, and then raped her vaginally. Although Jackson’s rendition did not describe his use of the stun gun, evidence was presented at trial that he shocked Styles with a stun gun once above her left breast and several times in the pubic area. Jackson stated that he then moved away from Styles and looked at his pornographic magazine while masturbating. The tape over Styles’ mouth loosened, and Styles began screaming. Jackson walked up to her, put the gun to her head, and shot her once. That afternoon, Jackson went back to the K-Mart, returned the gun, and received a refund. Jackson was crying during his entire confession, and the report of his confession indicates that at times during the interview the officers could not understand his words. Jackson repeated many times that he did not mean to kill Styles. A search of Jackson’s home and cars, conducted pursuant to a search warrant, led investigators to recover a functional stun gun, a flashlight, a black “Ninja” outfit, a wrapper to an adult magazine, and a partially empty box of .22 caliber rifle bullets. Jackson was charged in Buncombe County with first-degree murder, first-degree kidnapping, and first-degree rape. After the trial court denied Jackson’s pretrial motion to suppress his confession, a jury returned a guilty verdict on all three charges. On the jury’s recommendation, the court imposed the death penalty for the murder conviction and prison sentences for the rape and kidnapping convictions. On appeal, the North Carolina Sü-preme Court reversed Jackson’s conviction and ordered a new trial, concluding that police had violated Jackson’s Miranda right not to be interrogated after he had invoked his right to counsel. State v. Jackson, 348 N.C. 52, 497 S.E.2d 409, 412 (1998). On March 3, 2000, Jackson pled guilty in State court to second-degree murder, first-degree rape, and second-degree kidnapping. The stipulated prison sentences in the agreement totaled over 31 years, and Jackson received credit for 5 years already served. At the time of Jackson’s plea, none of his lawyers considered the possibility of a federal prosecution, and none advised Jackson that he could be subject to federal prosecution. On November 6, 2000, a federal grand jury returned a superseding bill of indictment charging Jackson, in one count, of using a firearm during and in relation to a crime of violence, specifically murder, kidnapping, and aggravated sexual abuse, in violation of 18 U.S.C. § 924(j)(l). At trial, the government called 22 witnesses during the guilt phase and introduced extensive physical and testimonial evidence, including Jackson’s confession, which was received without objection. The jury returned a guilty verdict and then proceeded to consider the appropriate sentence. During the sentencing phase, the government presented the testimony of the victim’s mother, Kathleen Styles, and the defense presented the testimony of Jackson’s adoptive mother, Sally Jackson. The defense also attempted to offer the testimony of the adoptive parents of Jackson’s natural sister, who suffered behavioral disorders, but the district court did not allow this testimony without any expert testimony linking the sister’s mental condition to Jackson’s. To rebut Sally Jackson’s testimony, the government played for the jury, over Jackson’s objection, portions of a videotaped interview given by Jackson for FOX News in October 2000, after his State conviction had been reversed and he had been sentenced pursuant to a guilty plea. The jury found unanimously that the government had proved beyond a reasonable doubt four aggravating factors, including the fact that Karen Styles’ death occurred during the commission of the offense of kidnapping, as defined under 18 U.S.C. § 1201, and the fact that Jackson committed the crime in an “especially heinous, cruel or depraved manner in that it involved torture or serious physical abuse to Karen Styles.” Various jurors found 14 mitigating circumstances, and the jury found unanimously that “the aggravating factor or factors found to exist sufficiently outweigh[ed] all the mitigating factor or factors found to exist to justify a death sentence.” All 12 jurors signed the verdict form, unanimously recommending that Jackson be sentenced to death. In accordance with that recommendation, the district court entered judgment on May 14, 2001, finding Jackson guilty of the offense charged in the indictment and imposing the sentence of death. The judgment also provided: “This judgment is effective immediately and is neither consecutive to nor delayed by the judgment and sentence previously imposed by the State of North Carolina.” This appeal followed. II Jackson’s most significant argument on appeal is that, under 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), his indictment was defective because it did not allege aggravating factors necessary to the imposition of the death penalty and that the failure to allege an essential element in the indictment cannot be deemed harmless error. With some foresight at the time, Jackson moved in the district court to dismiss the indictment because it failed to allege “the existence of any of the 16 statutory aggravating factors set out in 18 U.S.C. § 3592(c).” (Emphasis added). In rejecting this argument, the district court stated: [T]he indictment clearly charges the Defendant with (1) intentionally using a firearm and thereby causing the death of Karen Styles; (2) intentionally shooting her with the firearm; (3) acting with premeditation in the perpetration of an act of violence; (4) the death occurred during the commission of kidnapping; (5) he subjected her to aggravated sexual abuse during the commission of the offense; and (6) he acted with malice aforethought and premeditation. While the language of the indictment is not identical to the language of the notice of intent to seek the death penalty, it contains all the elements necessary under the federal death penalty statute to charge a capital crime. The court also ruled, in the alternative, that Congress did not make aggravating circumstances statutory elements of an underlying offense. The court stated, “[T]he statutes at issue expressly authorize a maximum penalty of death and the sentencing factors of mental culpability and aggravating circumstances do not increase the sentencing range but rather provide the particularized standards for choosing which of the alternative available sentences should be imposed.” (Quoting United States v. Allen, 247 F.3d 741, 763 (8th Cir.2001), and citing Walton v. Arizona, 497 U.S. 639, 648, 110 S.Ct. 3047, 111 L.Ed.2d 511 (1990)). On appeal, Jackson preserved his argument, reasoning from the Supreme Court’s decision in Apprendi that “a question emerges as to the constitutionality of an indictment in a capital case that omits any aggravating circumstances that ultimately lead to the defendant’s death sentence.” Recognizing that the Supreme Court’s decision in Walton had rejected his argument, Jackson nevertheless argued in his opening brief that in light of Apprendi, “the validity of the plurality’s view in Walton is questionable.” After Jackson submitted his opening brief but before he submitted his reply brief, the Supreme Court overruled Walton in Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002). Accordingly, in his reply brief, Jackson expanded his argument, in light of Ring, contending that because the government relied on multiple aggravating circumstances to obtain the death penalty, all of them must be alleged in the indictment. In laying the foundation for this argument, Jackson stated: Section 3593 [of Title 18] requires not only that the jury find at least one aggravating circumstance beyond a reasonable doubt, but also (1) that the jury find all the aggravating factors outweigh any mitigating factors and (2) that the jury find the death sentence is appropriate in light of all the aggravating factors. Until the jury finds the aggravating factors outweigh the mitigating factors and that the death sentence is appropriate in light of all the aggravating factors, the death sentence is not an available punishment. Resting on this sentencing scheme, Jackson concluded that “[b]ecause the totality of the aggravating factors increase the authorized punishment for Jackson, all of the aggravating factors must be raised in the indictment. Because the indictment was deficient, the judgment of death cannot stand.” (Emphasis added). Jackson was correct in forecasting that, because of Apprendi, Walton’s days were numbered. The defendant in Apprendi pleaded guilty to possession of a firearm under New Jersey law, which carried a maximum sentence of 10 years’ imprisonment. During sentencing, however, the sentencing judge found, by a preponderance of the evidence, that Apprendi’s crime had been motivated by racial animus with the purpose to intimidate, thus making Apprendi eligible for a hate-crime sentence enhancement. With the enhancement, Ap-prendi faced a maximum sentence on the firearm count of 20 years. The court actually sentenced Apprendi on that count to 12 years’ imprisonment, which exceeded the 10-year maximum for a violation without the hate-crime enhancement. The Supreme Court concluded that the trial judge’s factfinding and imposition of the hate-crime sentencing enhancement violated Apprendi’s Sixth Amendment jury trial right because, “[o]ther than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt.” Apprendi, 530 U.S. at 490, 120 S.Ct. 2348. The Court described longstanding historical practice indicating that “facts that expose a defendant to a punishment greater than that otherwise legally prescribed were by definition ‘elements’ of a separate legal offense.” Id. at 483 n. 10,120 S.Ct. 2348. New Jersey defended against Appren-di’s constitutional attack with the assertion that the hate-crime enhancement was not an element of the offense but rather a sentencing factor to guide the judge’s discretion. The Supreme Court rejected this argument because the legislature’s own characterization of the enhancement as an element or a sentencing factor is not determinative: “[T]he relevant inquiry is one not of form, but of effect — does the required finding expose the defendant to a greater punishment than that authorized by the jury’s guilty verdict?” Id. at 494, 120 S.Ct. 2348. Again, “merely because the state legislature placed its hate crime sentence ‘enhancer’ within the sentencing provisions of the criminal code does not mean that the finding of a biased purpose to intimidate is not an essential element of the offense.” Id. at 495, 120 S.Ct. 2348 (quotation marks and citation omitted). Accordingly, Apprendi stands for the principle that regardless of the legislature’s characterization of a factor as a “sentence enhancement” or an “element,” the appropriate characterization of that factor under the Constitution depends on how the factor functions. “[W]hen the term sentence enhancement’ is used to describe an increase beyond the maximum authorized statutory sentence, it is the functional equivalent of an element of a greater offense than the one covered by the jury’s guilty verdict.” Id. at 494 n. 19,120 S.Ct. 2348. When the Supreme Court applied the holding of Apprendi to Arizona’s capital sentencing scheme, it concluded, in Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), that to the extent the Arizona sentencing scheme permits a sentencing judge, sitting without a jury, to find an aggravating factor essential for the imposition of a death penalty, it violates the Sixth Amendment. Arizona’s first-degree murder statute provided that the offense “is punishable by death or life imprisonment as provided by § 13-703.” Ariz.Rev.Stat. Ann. § 13~1105(C) (West 2001). The cross-referenced § 13-703 required the trial judge to hold a separate hearing to determine the existence and relative weight of aggravating and mitigating circumstances and provided that “[t]he court alone shall make all factual determinations required by this section.” Id. § 13-703. Summarizing the operation of this scheme, the Court stated: Based solely on the jury’s verdict finding Ring guilty of first-degree felony murder, the maximum punishment he could have received was life imprisonment. This was so because, in Arizona, a death sentence may not legally be imposed unless at least one aggravating factor is- found to exist beyond a reasonable doubt. Ring, 122 S.Ct. at 2437 (quotation marks, ellipsis, and citations omitted). Because “ ‘the core crime and the aggravating fact together constitute an aggravated crime,’ ” Ring, 122 S.Ct. at 2441 (quoting Apprendi, 530 U.S. at 501, 120 S.Ct. 2348 (Thomas, J., concurring)), the aggravating factor operates as “ ‘the functional equivalent of an element of a greater offense,’ ” id. (quoting Apprendi, 530 U.S. at 494 n. 19, 120. S.Ct. 2348). The Ring Court reiterated the Ap-prendi principle that “[i]f a State makes an increase in a defendant’s authorized punishment contingent on the finding of a fact, that fact — no matter how the State labels it — must be found by a jury beyond a reasonable doubt.” Id. at 2439. In his concurring opinion in Ring, Justice Scalia explained: What today’s decision says is that the jury must find the existence of the fact that an aggravating factor existed. Those States that leave the ultimate life- or-death decision to the judge may continue to do so — by requiring a prior jury finding of aggravating factor in the sentencing phase or, more simply, by placing the aggravating-factor determination (where it logically belongs anyway) in the guilt phase. Id. at 2445 (Scalia, J., concurring). Thus, under Apprendi and Ring, when a factual finding of at least one aggravating factor is necessary to the imposition of a death sentence, the aggravating factor functions as an element of an aggravated offense — e.g., first-degree murder with an aggravating factor — and must be found by the jury, as guaranteed by the Sixth Amendment. The Supreme Court did not, however, address the scope of the Fifth Amendment Indictment Clause in Ring because that case came from a State system and the Fifth Amendment Indictment Clause has not been incorporated against the States. See Ring, 122 S.Ct. at 2437 n. 4. Nonetheless, Jackson argues that the holding in Ring requires that an aggravating factor necessary to the imposition of the federal death penalty must also be alleged in the indictment. We agree. The Fifth Amendment provides that “[n]o person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury.” U.S. Const, amend. V. The traditional rule for the sufficiency of an indictment is that it contain all elements of the offense charged to give notice to the defendant of the charge to which he must plead. Hamling v. United States, 418 U.S. 87, 117, 94 S.Ct. 2887, 41 L.Ed.2d 590 (1974) (“[A]n indictment is sufficient if it, first, contains the elements of the offense charged and fairly informs the defendant of the charge against which he must defend, and, second, enables him to plead an acquittal or conviction in bar of future prosecutions for the same offense”); see also United States v. Carrington, 301 F.3d 204, 209-10 (4th Cir.2002). Jackson does not dispute, on appeal, that his indictment contained all the statutory elements necessary to allege a violation of 18 U.S.C. § 924(j)(l), the basic offense for which he was charged and convicted. Nor does he dispute that § 924(j)(l) carries with it the potential penalty of death. But he maintains that just as the aggravating factors essential to qualify his violation for the death penalty must be found by the jury under Apprendi and Ring, they too must be alleged in the indictment as elements of an aggravated offense. It is no doubt true, as a general principle, that the Fifth Amendment right to be charged by an indictment containing every element of the offense is no less demanding than the Sixth Amendment right to have every element of the offense found by the jury. See Harris v. United States, 536 U.S. 545, 122 S.Ct. 2406, 2418, 153 L.Ed.2d 524 (2002) (“The grand and petit juries thus form a strong and two-fold barrier between liberties of the people and the prerogatives of the [government]”) (quotation marks, ellipsis, and citation omitted). Under this symmetry between indictment and factfinding, the indictment, which serves as a notice-giving document, must charge each element on which the factfin-der must focus to determine the defendant’s innocence or guilt on the charge. “A crime [is] not alleged, and a criminal prosecution not complete, unless the indictment and the jury verdict includes] all the facts to which the legislature ha[s] attached the maximum punishment.” Harris, 122 S.Ct. at 2417. Although Apprendi and its progeny have identified a circumstance in which a fact that the legislature has characterized as a sentencing factor must, as a matter of constitutional imperative, be treated as an element — i.e., when that fact increases the potential punishment beyond the statutory maximum — these cases have not obliterated all distinctions between sentencing factors and elements. The Court in Harris explained the distinctions. In Harris, the Supreme Court held that it was permissible for a judge to find a fact that triggers a mandatory minimum sentence as long as that minimum sentence does not exceed the maximum penalty under the statute. The Court construed 18 U.S.C. § 924(c)(1)(A), which criminalizes the use or carrying of a firearm in relation to a crime of violence or drug trafficking and stipulates a minimum sentence of five years if the gun is not brandished or discharged, a mandatory minimum of seven years if the gun is brandished, and a mandatory minimum of ten years if the gun is discharged. According to the Court, this statute described a single offense, and the fact of brandishment or discharge was a sentencing factor, not an element of the crime that needed to be charged in the indictment or submitted to the jury for proof beyond a reasonable doubt. In reaching that conclusion, the Court began its analysis with the recognition that “any fact extending the defendant’s sentence beyond the maximum, authorized by the jury’s verdict would have been considered an element of an aggravated crime — and thus the domain of the jury — by those who framed the Bill of Rights.” Id. at 2414 (emphasis added). The Court stated further that this right to have such elements found by a jury, and indeed alleged in the indictment, was not something that Congress could bypass through statutory labeling: Congress may not manipulate the definition of a crime in a way that relieves the Government of its constitutional obligations to charge each element in the indictment, submit each element to the jury, and prove each element beyond a reasonable doubt. Id. at 2414. The Harris Court explained, however, that the indictment need not allege all facts altering the range of the sentence to which the individual defendant may be exposed, so long as that range is within the maximum range justified by the charge and the verdict of the jury on that charge. It explained, “Judicial factfinding in the course of selecting a sentence within the authorized range does not implicate the indictment, jury-trial, and reasonable-doubt components of the Fifth and Sixth Amendments.” Id. at 2415. Rather, the indictment only needs to charge those facts that will make defendants aware of the “heaviest punishment” that they might receive if convicted. Id. at 2416. Summarizing this principle, the Court stated: Whether chosen by the judge or the legislature, the facts guiding judicial discretion below the statutory maximum need not be alleged in the indictment, submitted to the jury, or proved beyond a reasonable doubt. Id. at 2418; see also Proffitt v. Florida, 428 U.S. 242, 252, 96 S.Ct. 2960, 49 L.Ed.2d 913 (1976) (plurality opinion) (“[I]t has never [been] suggested that jury sentencing is constitutionally required”). In sum, if the governing statute provides that an aggravating factor must exist to justify the imposition of the death penalty, the statute provides for an “aggravated” offense and the indictment must therefore give notice of and charge the existence of the aggravated offense. Accordingly, in this case, the analysis begins by looking at the statute under which Jackson was indicted to determine whether it provides for an aggravated offense. Jackson’s indictment charged a violation of 18 U.S.C. § 924(j)(l), which provides: A person who, in the course of a violation of subsection (c) [using or carrying a firearm during and in relation to any crime of violence], causes the death of a person through the use of a firearm, shall — (1) if the killing is murder (as defined in section 1111), be punished by death or by imprisonment for any term of years or for life. As used in that section, murder is defined as: the unlawful killing of a human being with malice aforethought. Every murder perpetrated by poison, lying in wait, or any other kind of willful, deliberate, malicious, and premeditated killing; or committed in the perpetration of, or attempt to perpetrate, any arson, escape, murder, kidnapping, treason, espionage, sabotage, aggravated sexual abuse or sexual abuse, burglary, or robbery; or perpetrated from a premeditated design unlawfully and maliciously to effect the death of any human being other than him who is killed, is murder in the first degree. 18 U.S.C. § 1111(a). While § 924(j)(l) authorizes punishment by a sentence of death or a term of imprisonment, Chapter 228 of Title 18 (18 U.S.C. §§ 3591-8598) dictates whether the death sentence for violation of § 924(j) may be imposed. Section 3591 authorizes the imposition of the death penalty only if a separate sentencing hearing is held pursuant to § 3593 in which the factfinder considers proof of mitigating and aggravating factors, as listed in § 3592. If the factfin-der finds that aggravating factors sufficiently outweigh all mitigating factors to justify a sentence of death or if aggravating factors, without any mitigating factors, are sufficient to justify a sentence of death, the factfinder is authorized to recommend the death penalty. 18 U.S.C. § 3593. If such a recommendation is made, the court must follow the recommendation and sentence the defendant to death. 18 U.S.C. § 3594. However, “[iff no aggravating factor set forth in section 3592 is found to exist, the court shall impose a sentence other than death authorized by law.” 18 U.S.C. § 3593(d) (emphasis added). Thus, § 924(j)(l) actually contains two offenses — a basic offense without any aggravating factor, the commission of which exposes the defendant to a maximum punishment of life imprisonment, and an aggravated offense with at least one aggravating factor, the commission of which exposes the defendant to the maximum punishment of the death sentence. Consequently, just as in the Arizona scheme where a “death sentence may not legally be imposed ... unless at least one aggravating factor is found to exist beyond a reasonable doubt,” Ring, 122 S.Ct. at 2487 (quotation marks and citation omitted), so too at least one aggravating factor is necessary for the imposition of the death penalty under the relevant federal statutory scheme in this case. And because the existence of at least one aggravating factor is necessary to impose the death sentence, the existence of at least one aggravating factor must be alleged in the indictment and that aggravating factor must be found by the jury as a required element for exposing the defendant to the death penalty- Thus, to impose the death sentence on Jackson in this case, the indictment must allege all elements of an aggravated offense, and because at least one aggravating factor is necessary to charge such an offense, the indictment must allege that at least one aggravating factor exists. Reaching this conclusion, however, does not mean that all sentencing factors must be included in the indictment. Harris explicitly states otherwise. See Harris, 122 S.Ct. at 2418. Rather, when the death penalty is dependent on a finding of an aggravated offense, then the core statutory elements of that offense, as well as at least one aggravating factor, must be charged in the indictment and found by the jury. But it should be understood that the finding of guilt on such an indictment does not ineluctably lead to the imposition of the death penalty. Instead, the indictment assures that a verdict is returned on an offense for which the sentence of death is available. Congress has committed the decision whether to impose that penalty to the sentencer, who remains free during the sentencing phase to impose the death sentence or some lesser sentence after hearing evidence regarding sentencing factors, both aggravating and mitigating. With these applicable principles stated, Jackson’s arguments may now be reviewed. First, in his motion to dismiss the indictment, filed in the district court, Jackson contended that the indictment was defective because it did not allege “the existence of any of the 16 statutory aggravating factors.” (Emphasis added). The district court, finding the allegation of at least two statutory aggravating factors, denied Jackson’s motion. And insofar as Jackson appeals the denial of that motion, affirmance is required. The indictment returned by the grand jury against Jackson provided that on or about October 31, 1994, in the Pisgah National Forest (in western North Carolina), Jackson: did unlawfully, knowingly, and intentionally use and carry a firearm, to wit: a .22 caliber rifle, during and in relation to a crime of violence for which he may be prosecuted in a court of the United States, to wit: Murder (Title 18 United States Code, Section 1111(a)), Kidnapping (Title 18 United States Code, Section 1201(a)(2)), and Aggravated Sexual Abuse (Title 18 United States Code, Section 2241(a)(l)(2)), in violation of Title 18 United States Code, Section 924(c)(1), and, in the course of such violation and through the use of such firearm, did cause the death of a person, Karen Styles, in violation of Title 18 United States Code, Section 924(j)(l), which killing is a murder as defined in Title 18 United States Code, Section 1111, in that RICHARD ALLEN JACKSON unlawfully killed a human being, Karen Styles, with malice aforethought, by shooting her with the firearm willfully, deliberately, maliciously, and with premeditation, and in the perpetration and attempted perpetration of a felony, to wit: kidnapping and aggravated sexual abuse. This indictment must be read to charge Jackson with use of a firearm in the commission of first-degree murder with at least two aggravating factors. Section 3592(c) of Title 18 provides a list of aggravating factors that can justify imposition of the death penalty. Jackson’s indictment alleged aggravating factor one from this list, “death during commission of another crime,” inasmuch as the indictment alleged that the murder occurred during the perpetration of kidnapping, in violation of 18 U.S.C. § 1201. See 18 U.S.C. § 3592(c)(1). In addition, aggravating factor six, which exists when the defendant is found to have “committed the offense in an especially heinous, cruel, or depraved manner in that it involved torture or serious physical abuse to the victim,” was also adequately alleged. See 18 U.S.C. § 3592(c)(6). Aggravated sexual abuse, which is alleged in the indictment, would appear to satisfy “serious physical abuse to the victim.” Under 18 U.S.C. § 2241, which states the offense of “aggravated sexual abuse,” a person commits the offense when he “knowingly causes another person to engage in a sexual act ... by using force against that other person; or ... by threatening or placing that other person in fear that any person will be subjected to death, serious bodily injury or kidnapping; or attempts to do so.” Because Jackson’s motion below to dismiss the indictment was based on his claim that it did not include any aggravating factors necessary for imposition of the death penalty, the motion was correctly denied for the reasons given by the district court. On appeal, Jackson also makes a new argument in light of the Supreme Court’s decision in Ring, contending that “[because the totality of the aggravating factors increase the authorized punishment for Jackson, all of the aggravating factors must be raised in the indictment.” (Emphasis added). Jackson, however, did not present this argument to the district court, and accordingly it was forfeited. See Car-rington, 301 F.3d at 208. Such forfeited claims of error are reviewed under the plain-error test established under Federal Rule of Criminal Procedure 52(b), which is articulated as follows: “Under that test, before an appellate court can correct an error not raised at trial, there must be (1) ‘error,’ (2) that is ‘plain,’ and (3) that ‘affect[s] substantial rights.’ ” Johnson v. United States, 520 U.S. 461, 466-67, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997) (quoting [United States v.] Olano, [507 U.S. 725], 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 [ (1993) ]). “If all three conditions are met, an appellate court may then exercise its discretion to notice a forfeited error, but only if (4) the error seriously affeet[s] the fairness, integrity, or public reputation of judicial proceedings.” 520 U.S. at 467,117 S.Ct. 1544 (internal quotation marks omitted) (quoting Olano, supra, at 732, 113 S.Ct. 1770). United States v. Cotton, 535 U.S. 625, 122 S.Ct. 1781, 1785, 152 L.Ed.2d 860 (2002). To carry his burden under the plain-error test, Jackson contends that it was error to have sentenced him to death on an indictment that did not allege all of the aggravating factors presented by the government to the jury to return the death penalty. The notice of intent to seek the death penalty, served on Jackson pursuant to 18 U.S.C. § 3593(a), listed five aggravating factors — three as listed in §§ 3592(c)(1), (6), and (9), and two non-statutory factors. The government submitted four of the five factors to the jury. Only the first aggravating factor, that the victim’s death occurred during the commission of a crime (kidnapping) and the second, that the offense was committed in an “especially heinous, cruel, or depraved manner in that it involved torture or serious physical abuse of the victim,” were alleged in the indictment. Thus, two aggravating factors submitted to the jury during sentencing were not alleged in the indictment. In arguing that this omission amounted to a fatal defect in the indictment, Jackson confuses a necessary element with sentencing facts. Ring held that if an aggravating factor is statutorily necessary to the imposition of the death penalty, a distinct aggravated offense is created for which the death penalty is an available sentence, and, to find the defendant guilty on that offense “at least one” factor must be found by the factfinder. Ring, 122 S.Ct. at 2443. It follows that if an aggravating factor is an element of the aggravated offense, then to charge the offense, the existence of an aggravating factor must be alleged. See Harris, 122 S.Ct. at 2417. The defendant is by such an allegation given notice that a conviction on the indictment authorizes imposition of the death penalty. But for the purpose of charging the aggravated offense for which the heaviest punishment is available, only the fact that an aggravating factor exists to justify the penalty needs to be alleged, consistent with the role of the indictment. Id. at 2416. As long as the heaviest punishment is justified by a conviction on the offense charged in the indictment, any other facts relevant to sentencing are subject to “[jjudicial fact-finding in the course of selecting a sentence within the authorized range,” and such factfinding “does not implicate the indictment” requirements of the Fifth Amendment. Id. at 2415. In this case, because the applicable statute requires that at least one aggravating factor be found to justify imposition of the death penalty, 18 U.S.C. § 3593(d), at least one must be alleged to charge the aggravated crime for which the death penalty is authorized. The “core crime” of using a gun for murder with the additional fact that at least one aggravating factor exists constitutes “the aggravated crime.” And thus, only if the aggravated crime is charged may the jury also consider the sentence of death. In this case, the indictment did allege at least one aggravating factor so that the indictment charged an aggravated crime, and therefore, on conviction, the “heaviest punishment” of death could be, but need not be, imposed. See Ring, 122 S.Ct. at 2437 n. 4 (quoting Proffitt, 428 U.S. at 252, 96 S.Ct. 2960). The logic of Harris dictates that once the heaviest punishment is justified by a jury verdict of guilty on an indictment alleging an aggravated offense carrying the potential punishment of death, whether to impose the death penalty becomes the product of the sentencing fact-finding prescribed by 18 U.S.C. § 3593. See 122 S.Ct. at 2418. (“The Fifth and Sixth Amendments ensure that the defendant ‘will never get more punishment than he bargained for when he did the crime,’ but they do not promise that he will receive ‘anything less’ than that”) (quoting Apprendi 530 U.S. at 498, 120 S.Ct. 2348 (Scalia, J., concurring)). Thus, Jackson has not demonstrated that the omission of all of the aggravating factors was error, much less plain error. See Cotton, 122 S.Ct. at 1785. Accordingly, this new argument raised for the first time on appeal must be rejected. In addition to his arguments relating to the indictment’s failure to allege aggravating facts, Jackson contends that the allegations of the indictment that referred to kidnapping as an aggravating factor were insufficient because the indictment did not recite all the elements of the underlying crime of kidnapping, as defined by 18 U.S.C. § 1201. This argument, too, is without merit. Established rules of pleading in an indictment do not require that each term or fact be fully defined, so long as the defendant is provided fair notice of the elements of the offense with which he is charged and sufficient detail so that he can plead an acquittal or a guilty verdict as a bar to a subsequent prosecution for the same offense. See Hamling, 418 U.S. at 117, 94 S.Ct. 2887; Carrington, 301 F.3d at 209-10. But while it is true that an indictment must include all the elements of an offense, these elements may employ the statutory language defining the offense. See, e.g., United States v. Wicks, 187 F.3d 426, 427 (4th Cir.1999) (“Generally, an indictment is sufficient if it alleges an offense in the words of the statute, assuming those words fully, directly, and expressly, without any uncertainty or ambiguity, set forth all the elements necessary to constitute the offense”) (quotation marks and citations omitted). In this case, Jackson was charged with the offense set forth in 18 U.S.C. § 924(j)(l), coupled with the fact that the violation involved an aggravating factor to justify the imposition of the death penalty. The crime is charged simply by alleging all the elements of the murder together with a sufficient disclosure of an aggravating factor to inform the defendant of the crime charged. One aggravating factor identified in Jackson’s indictment is the commission of the crime of kidnapping, as specified by 18 U.S.C. § 1201. Jackson does not dispute that the indictment fairly describes a violation of § 924(j)(l) and of 18 U.S.C. § 1111(a), defining first-degree murder. Nor can he dispute the fact that the indictment alleges that the death resulting from the charged offense occurred during the commission of a felony, i.e., kidnapping as specified in 18 U.S.C. § 1201(a)(2). His only complaint is that the elements of kidnapping are not also set forth. But kidnapping is not the offense with which Jackson was charged. Rather, the fact that death occurred during a kidnapping is only an element of the aggravated offense with which he was charged. The reference to kidnapping together with a specific reference to the statutory definition of the crime adequately informs Jackson of the particular element of the aggravated crime, that an aggravating factor existed. See Wicks, 187 F.3d at 427. We therefore also reject this argument. In sum, the indictment in this case properly charged Jackson with the use of a firearm during and in relation to first-degree murder, in violation of 18 U.S.C. § 924(j)(l), coupled with the existence of the aggravating factor that the death occurred during the commission of the offense of kidnapping, as defined in 18 U.S.C. § 1201(a)(2). And because the indictment alleged at least one aggravating factor, it charged the aggravated crime for which a sentence of death could be, but need not be, imposed. See 18 U.S.C. §§ 3592(c)(1), 3593(d). For these reasons, Jackson’s arguments that the indictment was defective must be rejected. Ill Jackson also raises a significant issue in contending that the district court erred during the sentencing phase in admitting, over his objection, an October 2000 videotaped interview of Jackson for FOX News in rebuttal to the testimony of Sally Jackson, Jackson’s adoptive mother and the only witness Jackson offered during the penalty phase. Jackson argues that the videotape went “far afield of proper rebuttal,” amounting to “a rambling diatribe by defendant on a whole host of issues, including derogatory comments about State prosecutors.” He maintains that the admission of this “highly inflammatory information” was prejudicial. In response, the government argues that the videotape evidence was offered to rebut Sally Jackson’s testimony describing Jackson’s childhood problems, his failures, mental health, learning difficulties, and social interaction skills, as well as his marital problems. To the extent that these problems provided mitigation of his conduct, the government sought, through the videotape, to demonstrate that actually Jackson’s home life was positive, that he was intelligent and articulate, and that he was functioning at a far more normal level during the relevant periods than was described by Sally Jackson. The government maintains that the evidence was “classic rebuttal evidence.” Alternatively, it argues that “any perceived error” would be harmless because “the facts of the crime, standing alone, amply supported the jury’s decision[ ]” to recommend the death sentence. Sally Jackson testified about Richard Jackson’s childhood, his adolescence, his education, his work experience, his problems and failures, his marriage, and his activities in the month preceding the murder of Karen Styles and in the several months thereafter. She explained that she and her husband adopted Richard when he was five-and-a-half years old and that they were struck immediately by his abnormal behavior and his use of inappropriate language. She testified that by the time Richard was six or seven, he was caught several times masturbating. Sally Jackson testified that, beginning when Richard was 18 or 14 years old, he would often become depressed, and he tried to kill himself several times by overdosing on over-the-counter medications. When he overdosed, Sally Jackson stated that she would have discussions with Richard, and Richard was “always sorry that he did it, but always promised he would never do it again.” During the time that Sally Jackson and her husband were raising Richard, she described how Richard was always loved and how they helped him through crises. She described repeatedly the fact that their household was governed by love, although filled with problems involving Richard. During high school, Richard did not participate in sports and when he finally participated in an activity, the debate club, it was a failure. At the first debate, Richard embarrassingly rambled on about matters not relevant to the issue at hand. Sally Jackson regretted that Richard had not shared the written materials about the debate issue with her or her husband so that they could have read them and gone over them with Richard before the debate. Richard also did poorly in high school, “not well at all,” receiving grades of Cs and Ds — “barely passing.” Sally Jackson testified that after Richard graduated from high school, he spent six weeks in the Navy before he left because of a mental problem and returned to Asheville, North Carolina. Sally Jackson testified that Richard married his wife, Donna, just a few days after they first met and, thereafter, had two children within a short period of time. While Richard had difficulty holding a job, he did work somewhat successfully at the pizza shop where he met Donna and later worked at Mountain View Restaurant, which was owned by his adoptive father, J.D. Jackson. Richard and his family lived in a trailer behind the Mountain View Restaurant. Sally Jackson testified that in the month prior to the murder of Karen Styles, Richard’s hygiene was increasingly worse, such that she would have to talk him into taking a bath to relieve his bad odor. She also testified that Richard suffered a serious burn on his arm a few days prior to the murder and was treated at the emergency center with strong pain medication. Sally Jackson acknowledged that Richard and his wife had financial problems and that she helped them pay the rent and sometimes the electricity. Some of their problems came from the fact that Richard ran up large telephone bills by calling 1-900 phone-sex numbers. Finally, Sally Jackson testified that on November 1, 1994, the day after Styles’ murder, Jackson was again admitted to the hospital, after having tried to commit suicide. After Richard was arrested in December 1994, Sally Jackson visited him in jail, and there was an emotional reunion. Everybody was crying, and there was the suggestion that Reverend Sexton was present, although Sally Jackson did not recall. She testified that she always wanted to believe that Richard did not kill Karen Styles, but in fact she came to believe that he did. Sally Jackson explained how she and her husband thereafter sought to contact the Styles family to express their sorrow and compassion, but they were never able to do so. A complete review of Sally Jackson’s testimony leads to the conclusion that the jury could have received the impression that Richard Jackson was not smart, that he had mental problems, including sexual problems, that he was loved as a child and reacted with love, trying to overcome his mental disabilities, and that he was remorseful whenever he did wrong. This, in particular, was revealed by the testimony of Richard’s apologies to his mother when he repeatedly attempted to commit suicide, the testimony of Richard’s attempt to commit suicide after the murder of Styles, and the testimony of his crying in the jail when he was visited by Sally Jackson with a minister, as well as Sally Jackson’s own remorseful approach, intending to visit the victim’s family. The government believed that a videotape of Richard’s interview with FOX News in October 2000 would rebut these impressions, and it offered the videotape into evidence, which the court received over Jackson’s objection. Jackson maintained that the videotape went beyond the scope of Sally Jackson’s testimony. The videotape reveals an articulate, intelligent, perhaps even manipulative, person who converses quickly, anticipating questions and where they might be leading. During the course of the interview, Jackson talked playfully and confidently, bantering with the reporter and cameraman and seeking to win their confidence. He filled his answers, which were long and rambling, with small jokes at which he himself laughed. He also was aware of the presence of the camera and the fact that it represented the “people out there.” During the course of the interview, Jackson made moral pronouncements about why he would not do things and why he would. For instance, he stated that he left the Navy because he did not want to be involved in killing, among other reasons. He also talked intelligently of his moral responsibilities to his wife and his children’s support. During the course of the interview, Jackson denied any involvement in the murder and ridiculed the government’s case, suggesting not only that the government bungled its handling of evidence that it had but also that it suppressed exculpatory evidence, including DNA evidence. Jackson took several opportunities to denounce government investigators and prosecutors, claiming that they were attempting to frame him. The interview also revealed Jackson’s distrust for politicians who, he stated, would say and do anything simply to get elected. In short, the Jackson who appeared in the videotape of his interview was not the mentally disabled, depressed, remorseful person who suffered from childhood problems, as portrayed by Sally Jackson. Rather it showed a manipulative, quick, and intelligent person who was angry with the government’s efforts to prosecute him for the Styles murder. While isolated statements and subjects discussed during the course of the interview could fairly be the subject of a challenge on the basis that the statements were not within the strict limits of the subjects to which Sally Jackson testified and thus were not reasonably “tailored” to what she said, see United States v. Stitt, 250 F.3d 878, 897 (4th Cir.2001), the videotape as a whole was substantially and reasonably within the range of rebutting the impression that Sally Jackson intended to leave with the jury. Although our rule in Stitt requires that rebuttal evidence be reasonably tailored to the evidence being rebutted, this is not to say that the evidence being rebutted must be taken in its most narrow probative range. To the contrary, any fact tended to be proved by the original evidence — whether directly, by inference, or by logic — can be rebutted. Our focus on what evidence may be offered in rebuttal must be directed at what is reasonably tailored to rebut the original evidence, including any inference that may fairly be drawn from it. In this case, Sally Jackson spoke directly and by inference to the jury regarding a majority of the 27 mitigating factors submitted by the defense for the jury’s consideration, and the videotape shown by the government was for the most part clearly relevant to rebuttal of a number of those on which Sally Jackson testified. Thus, there was “a nexus between the purported rebuttal evidence and the evidence that the purported rebuttal evidence seeks to rebut.” Id. Thus, the district court acted within its broad discretion in admitting the videotape in rebuttal. Even if portions of the tape went beyond the proper scope, i.e., they were not “reasonably tailored to the evidence [they sought] to refute,” Stitt, 250 F.3d at 897, any such error would be harmless. See 18 U.S.C. § 3595(c). The prosecution presented evidence in the case that Jackson kidnapped and bound up Styles with duct tape; that he painfully stimulated Styles with shocks from a stun gun in her pubic area multiple times; that he shot Styles in the head after raping her and masturbating to a pornographic magazine in front of her; and that his kidnapping, rape, and murder of Styles took a long period of time during which Styles undoubtedly suffered a great deal. The jury unanimously found all four aggravating factors submitted to it: (1) that the death of Karen Styles occurred during a kidnapping, (2) that Jackson committed the murder in an especially heinous, cruel, or depraved manner in that the murder involved torture or serious physical abuse, (3) that Jackson committed the murder after substantial planning and premeditation, and (4) that Jackson “caused injury, harm, and loss to Karen Styles’ family because of Karen Styles’ personal characteristics as an individual human being and the impact of her death upon her family.” The jury could not have relied on the videotape in finding any of these factors because the videotape contained no evidence regarding them. While the videotape might have persuaded the jury not to find some mitigating factors, these were factors touched on or developed through the testimony of Sally Jackson. Her testimony was broad-ranging, and the conclusions that could have been made based on it covered everything from Jackson’s childhood, his disabilities, his mental condition, his intelligence, his remorse, his ability to hold jobs, his social deficiencies, and more. Even if a given portion of the videotape might have made it less likely that the jury would have found some possible mitigating factor that was not covered by Sally Jackson’s testimony, the jury would have concluded beyond a reasonable doubt that the aggravating factors sufficiently outweighed the mitigating factors. The evidence in the record of the heinous nature of Jackson’s behavior was overwhelming, and the evidence in favor of mitigation was limited. Any portions of the tape that might have been found to be beyond the reasonable scope of Sally Jackson’s testimony, thus, did not change the outcome. IV We address Jackson’s remaining assignments of error in the order in which he has raised them. First, he contends that the government failed to overcome the presumption of a vindictive prosecution, created by the circumstances of his State conviction and his federal prosecution. He identifies multiple purported indicia of vindictiveness, including “[t]he federal government’s six-year delay, its sentencing the defendant to death after he had already received a 30-year State sentence, its refusal to honor and follow its own Petite policy, the violation of its own death penalty protocol, and its refusal to return Jackson to State custody as required by the writ and the interstate agreement on detainers, along with personal vindictiveness embedded in the prosecutor’s closing argument.” Because of the government’s failure to overcome the presumption of vindictiveness, he asserts, the indictment must be dismissed as vindictive. To establish prosecutorial vindictiveness, Jackson “must show, through objective evidence, that (1) the prosecutor acted with genuine animus toward the defendant and (2) the defendant would not have been prosecuted but for that animus.” United States v. Wilson, 262 F.3d 305, 314 (4th Cir.2001). If a defendant is unable to demonstrate the required animus, he may still present evidence of “circumstances from which an improper vindictive motive may be presumed.” Id. In describing when a given set of circumstances should give rise to a presumption of vindictiveness, we have articulated the principle that “such a presumption is warranted only when circumstances warrant it for all cases of the type presented.” Id. at 315. We have noted also that “the circumstances must be evaluated against the background presumption that charging decisions of prosecutors are made in the exercise of broad discretion and are presumed to be regular and proper.” Id. at 318. We can find nothing in this record that demonstrates the requisite animus to the defendant, nor can we find the circumstances giving rise to a presumption of such animus. The government’s delay in prosecution was based on its decision to defer to State authorities and to see whether federal interests would be vindicated. In this case, Jackson pleaded guilty on March 3, 2000, and was then sentenced, pursuant to a plea agreement, to slightly more than 30 years’ imprisonment, for which he received 5 years’ credit served during the prosecution of the case. Concluding that its interests were not vindicated, federal prosecutors initiated this case seven months later, on October 2, 2000. We conclude that no adverse inference could be drawn from this delay in these circumstances. Jackson also argues that the federal prosecutor’s decision to seek the death penalty after he had been