In United States v. Allen, 247 F.3d 741 (8th Cir.2001), we affirmed Billie Jerome Allen’s death sentence, rejecting, inter alia, his argument that his sentence violated the Fifth Amendment Indictment Clause. Id. at 761-64. The Supreme Court, at 536 U.S. 953, 122 S.Ct. 2653, 153 L.Ed.2d 830 (2002), granted Allen’s petition for writ of certiorari, vacated our decision, and remanded the case for reconsideration in light of Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002). On reconsideration, we hold that the indictment in Allen’s case failed to charge a federal capital offense, and that given Allen’s timely objections this failure cannot be dismissed as harmless error. Accordingly, we vacate the death sentence and remand to the district court for imposition of a life sentence.
I.
In 1997, Billie Jerome Allen and Norris G. Holder killed security guard Richard Heflin during an armed robbery of the Lindell Bank & Trust in St. Louis. Both were charged with violating 18 U.S.C. §§ 2, 2113(a) and (e) (1994) (armed robbery by force or violence in which a killing occurs) (Count I) and 18 U.S.C. §§ 2, 924(c)(1) and (j)(l) (1994 and Supp. II 1996) (carrying or using a firearm during a crime of violence and committing murder) (Count II). In separate jury trials, Allen and Holder were convicted on both counts. The jury sentenced Allen to life in prison on Count I and death on Count II. Prior to trial, at sentencing, and on direct appeal, Allen argued that a death sentence in his case would violate the Fifth Amendment Indictment Clause. Specifically, Allen argued that the government’s failure to allege in his indictment the mens rea specified in 18 U.S.C. § 3591(a)(2) and at least one aggravating factor from 18 U.S.C. § 3592(c), elements essential to a death sentence, was constitutional error in light of Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000).
We rejected Allen’s argument. At the time, our review of Supreme Court precedent and the Federal Death Penalty Act (FDPA) persuaded us that the mental culpability and aggravating factors were sentencing factors rather than elements of the offense. Allen, 247 F.3d at 762-64. This decision was premised on Walton v. Arizona, 497 U.S. 639, 110 S.Ct. 3047, 111 L.Ed.2d 511 (1990), in which the Supreme Court, in upholding a state capital sentencing scheme, deemed aggravating circumstances not separate penalties or offenses but rather “ ‘standards to guide the making of [the] choice between the alternative verdicts of death and life imprisonment.’ ” Id. at 648, 110 S.Ct. 3047 (quoting Poland v. Arizona, 476 U.S. 147, 156, 106 S.Ct. 1749, 90 L.Ed.2d 123 (1986)). Applying this reasoning to Allen’s case, we explained that Apprendi was not implicated, and the Fifth Amendment Indictment Clause not violated, because the statutes at issue exposed Allen to either death or a life sentence, and thus the mental culpability and aggravating factors “d[id] not increase the sentencing range but rather provide[d] the particularized standards for choosing which of the alternative available sentences should be imposed.” Allen, 247 F.3d at 763.
*748On June 24, 2002, the Supreme Court issued its decision in Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556. Overturning Walton in relevant part, the Court held that any fact essential to imposition of the death penalty must be submitted to a jury and found beyond a reasonable doubt, even where the statute at issue authorizes alternative sentences of life or death. Ring, 536 U.S. at 609, 122 S.Ct. 2428. Because Arizona’s death penalty could not be imposed without a finding of at least one aggravating factor, that factor operated as the functional equivalent of an essential element and could not be treated as merely a sentencing factor. Id.
The Supreme Court, at 536 U.S. 953, 122 S.Ct. 2653, 153 L.Ed.2d 830, subsequently granted Allen’s petition for writ of certio-rari, vacated our 2001 opinion, and remanded for reconsideration in light of Ring. On remand, we resolve the following question:
In light of Ring v. Arizona, was the indictment in this case sufficient to charge a capital offense, and, if not, must Allen’s death sentence be vacated because no aggravating factors were charged in the indictment?2
II.
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 government concedes that in light of Ring, Apprendi, and Jones v. United States, 526 U.S. 227, 119 S.Ct. 1215, 143
L.Ed.2d 311 (1999), the Supreme Court would likely hold that at least one statutory aggravating factor specified in 18 U.S.C. § 3592(c) must be alleged in Allen’s indictment. See Griffith v. Kentucky, 479 U.S. 314, 328, 107 S.Ct. 708, 93 L.Ed.2d 649 (1987) (stating that a new rule for criminal prosecutions applies to all cases pending on direct review). We agree. Just as the aggravating factors essential to qualify a particular defendant as death eligible must be found by the jury under Apprendi and Ring, they too must be alleged in the indictment. See Ring, 536 U.S. at 609, 122 S.Ct. 2428 (concluding that where a state statute requires the finding of a statutory aggravating circumstance before imposition of the death penalty, such facts “operate as ‘the functional equivalent of an element of a greater offense’ ”) (quoting Apprendi, 530 U.S. at 494 n. 19, 120 S.Ct. 2348); United States v. Cotton, 535 U.S. 625, 627, 122 S.Ct. 1781, 152 L.Ed.2d 860 (2002) (“In federal prosecutions, such facts [that increase the penalty for a crime beyond the prescribed statutory maximum] must also be charged in the indictment”) (citing Apprendi, 530 U.S. at 476, 120 S.Ct. 2348, and Jones, 526 U.S. at 243 n. 6, 119 S.Ct. 1215); Apprendi, 530 U.S. at 476, 490, 120 S.Ct. 2348 (applying principles “foreshadowed” in Jones to a state prosecution, and holding, on Fourteenth Amendment due process grounds, that “[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”);3 *749Jones, 526 U.S. at 243 n. 6, 119 S.Ct. 1215 (1999) (“[UJnder the Due Process Clause of the Fifth Amendment and the notice and jury trial guarantees of the Sixth Amendment, any fact (other than a prior conviction) that increases the maximum penalty for a crime must be charged in an indictment, submitted to a jury, and proven beyond a reasonable doubt.”). See also United States v. Jackson, 327 F.3d 273, 286-87 (4th Cir.2003) (Neimeyer, J., cone.) (concluding, after Ring, that an aggravating factor necessary to the imposition of the federal death penalty must also be alleged in the indictment); United States v. Higgs, 353 F.3d 281, 297 (4th Cir.2003) (“any factor required to be submitted to the jury must be included in the indictment”); United States v. Regan, 221 F.Supp.2d 672, 679 (E.D.Va.2002) (“[I]n light of Jones’s requirement that ‘any fact ... that increases the maximum penalty for a crime must be charged in an indictment,’ it appears to be a foregone conclusion that aggravating factors that are essential to the imposition of the death penalty must appear in the indictment.”) (quoting Jones, 526 U.S. at 243 n. 6, 119 S.Ct. 1215).
We start, then, from the premise that inclusion in Allen’s indictment of at least one statutory aggravating factor from 18 U.S.C. § 3592(c) was constitutionally mandated. See Apprendi, 530 U.S. at 490 n. 15, 120 S.Ct. 2348 (“The indictment must contain an allegation of every fact which is legally essential to the punishment to be inflicted.”) (quoting United States v. Reese, 92 U.S. 214, 232-33, 23 L.Ed. 563 (1875) (Clifford, J., dissenting) (emphasis added)). Allen argues that his indictment included no statutory aggravators and thus his death sentence cannot stand. The government defends the sentence on two grounds. First, the government argues that Allen’s indictment sufficiently alleged the requisite elements for imposition of the death penalty. Second, if error is found, the government argues that the error is harmless. We find neither argument persuasive.
A. Sufficiency of the Indictment
“To be sufficient, an indictment must ‘contain[ ] the elements of the offense charged.’” United States v. Olson 262 F.3d 795, 799 (8th Cir.2001) (quoting Hamling v. United States, 418 U.S. 87, 117, 94 S.Ct. 2887, 41 L.Ed.2d 590 (1974)). Where a statutory aggravating factor operates as the functional equivalent of an element, it too must be noticed in the indictment. Although the indictment “must be a plain, concise, and definite written statement of the essential facts constituting the offense,” Fed.R.Crim.P. 7(c)(1), it “need not be perfect, and common sense and reason prevail over technicalities.” United States v. Sabbeth, 262 F.3d 207, 218 (2d Cir.2001) (citation omitted). A challenge to the sufficiency of an indictment is reviewed de novo. United States v. White, 241 F.3d 1015, 1020 (8th Cir.2001).
The indictment at issue charged Allen and his co-defendant jointly in two counts. Count one charged a violation of 18 U.S.C. §§ 2, 2113(a) and (e), and alleged that the defendants
by force, violence, and intimidation did take from the person or presence of another, a quantity of United States currency, belonging to, and in the care, custody, control, management, and possession of the Lindell Bank & Trust Company, the deposits of which were then insured by the Federal Deposit Insurance Corporation; and in committing such offense did kill Richard Heflin.
*750Count two charged a violation of 18 U.S.C. §§ 2, 924(c)(1) and (j)(l), and alleged that the defendants
knowingly used and carried a firearm during and in relation to a crime of violence which may be prosecuted in a court of the United States, that is, bank robbery as alleged in Count I of this indictment and incorporated herein; and that in so doing [the defendants] committed murder as defined in 18 U.S.C. § 1111, that is, the unlawful killing of Richard Heflin with malice of forethought, such murder being willful, deliberate, malicious, premeditated, and committed in the perpetration of a robbery.
The government posits that in indicting Allen for bank robbery in Count I, and in incorporating the Count I bank robbery allegation in Count II, the count on which Allen received the death penalty, the grand jury indicted on one statutory ag-gravator, viz., that Allen committed the offense in the expectation of pecuniary gain. See 18 U.S.C. § 3592(c)(8) (“Pecuniary gain.-The defendant committed the offense as consideration for the receipt, or in the expectation of the receipt, of anything of pecuniary value.”). See also Fed. R.Crim.P. 7(c)(1) (authorizing incorporation of counts).
We are not persuaded that the indictment, even incorporating Count I into Count II, can fairly be read to state the essential facts which would constitute the pecuniary gain aggravator. Nothing in either count necessarily links the murder of Richard Heflin to the receipt of, or expectation of the receipt of, pecuniary gain. The fact that Allen and Holder robbed a bank “and in committing such offense did kill Richard Heflin,” as set forth in Count I, is insufficient given that bank robbery is not among the crimes which warrant automatic death qualification under 18 U.S.C. § 3592(c)(1).4 We agree with our sister circuits that the “offense committed” language in § 3592(c)(8) refers to murder, not the underlying felony, so that application of the pecuniary gain aggravating factor “is limited to situations where ‘pecuniary gain’ is expected ‘to follow as a direct result of the [murder].’ ” United States v. Bernard, 299 F.3d 467, 483 (5th Cir.2002) (alteration in original, and citation omitted); United States v. Chanthadara, 230 F.3d 1237, 1263 (10th Cir.2000) (citing supporting cases, and concluding that Congress’ exclusion of robbery from § 3592(c)(1) “suggests that the pecuniary gain aggravator applies when the murder itself was committed as consideration for, or in expectation of, anything of pecuniary value”). See also United States v. Cuff, 38 F.Supp.2d 282, 288 (S.D.N.Y.1999) (“[Section 3592(c)(8)] appeals] to be directed at a murder for hire or to collect insurance proceeds, or at least the sort of murder in which pecuniary gain can be expected to follow as a direct result of the crime. A murder from which pecuniary gain does not directly result would not appear to be within the reach of the statute.”). To hold otherwise would convert every felony murder in which the underlying felony had a pecuniary object or benefit into a federal capital offense. See Woratzeck v. Stewart, 97 F.3d 329, *751334-35 (9th Cir.1996) (construing Arizona pecuniary gain aggravator, and noting that “[e]ven if it is true that under many circumstances a person who kills in the course of a robbery is motivated to do so for pecuniary reasons, that is not necessarily so ... ”)• Like the other courts to have reviewed this issue, we find nothing in the statute or legislative history to suggest that Congress intended such a result.
We agree with the government that an indictment need not precisely track the language of the statute and is sufficient when it sets forth the facts that constitute the offense. There is nothing in this indictment, however, from which we can conclude that the grand jury in this case considered, and found, the facts that would support the pecuniary gain aggravator. See Olson, 262 F.3d at 799-800 (vacating conviction under 18 U.S.C. § 2113(a) where indictment did not sufficiently allege that the bank robbery was accomplished “by force and violence” as required by statute, and citation of the statute was not in itself sufficient to determine whether the grand jury considered the missing element in charging the defendant). Because Allen’s indictment cannot be reasonably construed to charge a statutory aggravating factor, as required for imposition of the death penalty, it is constitutionally deficient to charge a capital offense.
B. Harmless Error
The government argues that Allen’s death sentence should be affirmed because any error from the indictment omission was harmless. See Fed.R.Crim.P. 52(a) (“Any error, defect, irregularity, or variance which does not affect substantial rights must be disregarded.”); Delaware v. Van Arsdall, 475 U.S. 673, 681, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986) (“[A]n otherwise valid conviction should not be set aside if the reviewing court may confidently say, on the whole record, that the constitutional error was harmless beyond a reasonable doubt.”). The government contends that the failure to include a statutory aggravator did not affect Allen’s substantial rights because: (1) Allen had notice prior to trial that the government intended to seek the death penalty based on certain aggravating factors-thus Allen’s trial strategy was not hindered in any way by the error; and (2) given the lower evidentiary burden at the grand jury stage, it is beyond doubt that the grand jury would have found an aggravating factor had the government sought such an allegation.
We agree that this case does not present the notice problems that often accompany a deficient indictment, and we presume that the reliability of the verdict and sentence were not seriously affected by the error. Nevertheless, given the procedural posture of this case, and the error at issue, we conclude that the government did not meet its burden to prove beyond a reasonable doubt that the error was harmless. See United States v. Olano, 507 U.S. 725, 734, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993) (noting that where the defendant has made a timely objection to an error, the government bears the burden of persuasion with respect to demonstrating that the error was harmless); United States v. Anderson, 236 F.3d 427, 430 (8th Cir.2001) (affirming conviction and sentence where Apprendi error was harmless beyond a reasonable doubt).
Before discussing our harmless error determination, we first briefly address Allen’s contention that the error at issue here is of a type which can never be found harmless, and is, in fact “structural” error subject to automatic reversal. See Neder v. United States, 527 U.S. 1, 7, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (explaining that structural errors comprise a “limited class of fundamental constitutional errors that ‘defy analysis by “harmless error” standards,’ ” and which are “so intrinsical*752ly harmful as to require automatic reversal ... without regard to their effect on the outcome”) (internal quotation omitted). In response, the government argues that Neder precludes such a conclusion given that, in Neder, the Supreme Court did not include indictment error among the “very limited class” of structural error cases. See id. at 9,119 S.Ct. 1827 (citing Supreme Court precedent where structural error required automatic reversal, such as where there was a complete denial of counsel, a biased trial judge, racial discrimination in grand jury selection, denial of self-representation at trial, denial of a public trial, and a defective reasonable doubt instruction). The government posits that because indictment error is not structural, a defendant can only seek relief under Federal Rule of Criminal Procedure 52 (“Rule 52”) which requires a showing of prejudice.
We agree with Allen that the error at issue has some characteristics of a structural error, and, prior to Neder, most courts read Stirone v. United States, 361 U.S. 212, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960), as holding that a constructive amendment5 of an indictment can never be declared harmless. See United States v. Syme, 276 F.3d 131, 152 n. 7 (3d Cir.2002) (discussing constructive amendments, and referencing pre-Neder case law from the Second, Fourth, Ninth, and D.C. Circuits which deemed constructive amendments per se reversible under harmless error review). We agree with the government, however, that after Ned-er, such an argument is much more difficult to make. As we read Neder, it established a dichotomous framework for review of alleged constitutional error. An error is either structural, in which case, it is subject to automatic reversal regardless of its effect on the judicial proceedings, or it is subject to Rule 52 analysis which requires a finding of prejudice to the defendant. Thus, after Neder, it appears questionable whether there is such a thing as “per se reversible error” under a harmless error analysis. And a conclusion that indictment error is structural would require a very good explanation for why the Neder Court did not include any of its many Indictment Clause cases among those listed as examples of structural error, particularly given Stirone’s unequivocal language regarding the right to grand jury indictment. See Stirone, 361 U.S. at 217, 80 S.Ct. 270 (noting defendant’s “substantial right to be tried only on charges presented in an indictment returned by a grand jury’ ” and stating that “[deprivation of such a basic right is far too serious to be treated as nothing more than a variance and then dismissed as harmless error”).
We need not resolve this debate, however, because binding precedent in this circuit requires application of harmless error review under Rule 52. In United States v. Wright, 248 F.3d 765, 766-67 (8th Cir.2001) (per curiam), a panel of this court stated that “a violation of Jones, like a violation of Apprendi, ... is subject to harmless error analysis.” We discern nothing in Ring that would affect the standard of review adopted by this court in Wright. To the contrary, Justice O’Con-nor’s dissenting opinion in Ring forecast that many Ring-based challenges will fail *753“because the prisoners will be unable to satisfy the standards of harmless error or plain error review.” 536 U.S. at 621, 122 S.Ct. 2428. Thus, if, as we presume after Ring, a statutory aggravator operating as the functional equivalent of an essential element must be included in the indictment (as mandated by Jones), then Wright dictates that erroneous omission of that element, when properly objected to, is reviewed for harmless error.
1. The harmless error standard:
The harmless error standard of Rule 52(a) provides that “[a]ny error, defect, irregularity, or variance that does not affect substantial rights must be disregarded.” Fed.R.Crim.P. 52(a). Because Allen preserved his constitutional claim, the government bears the burden to prove beyond a reasonable doubt that the error was harmless, i.e., did not affect the defendant’s substantial rights.6 Neder, 527 U.S. at 19, 119 S.Ct. 1827; Olano, 507 U.S. at 734, 113 S.Ct. 1770. “[I]n most cases, [for an error to have affected substantial rights], it means that the error must have been prejudicial: [i]t must have affected the outcome of the district court proceedings.” Olano, 507 U.S. at 734, 113 S.Ct. 1770.7 See also United States v. Maynie, 257 F.3d 908, 919 (8th Cir.2001), cert. denied, — U.S. -, 124 S.Ct. 490, 157 L.Ed.2d 390 (2003), (“A defendant’s rights are substantially affected when the error ‘prejudicially influenced the outcome of the district court proceedings.’ ”) (quoting United States v. Butler, 238 F.3d 1001, 1005 (8th Cir.2001), in turn quoting United States v. Poulack, 236 F.3d 932, 938 (8th Cir.2001)).
Our determination of when error is prejudicial, i.e., has affected substantial rights, has involved somewhat variant approaches. In some cases, we have looked to the effect of the error on the sentence. In Maynie, we noted that “[i]n previous cases ... we have found a defendant’s substantial rights were affected where correction of the error would result in a lesser term of imprisonment.” 257 F.3d at 919 (citing, from this circuit, United States v. Kroeger, 229 F.3d 700, 702 (8th Cir.2000) (holding that error causing sentence to exceed authorized Guideline sentence by thirty months affects substantial rights), and United States v. Comstock, 154 F.3d 845, 850 (8th Cir.1998) (recognizing that substantial rights were “clearly affected” where defendant would serve seventeen months less if the error had not occurred); and citing, from other circuits, United States v. Robinson, 250 F.3d 527, 529 (7th Cir.2001) (noting there was “no question” an Ap-prendi error affected substantial rights where defendant’s sentence exceeded authorized sentence by twenty years); United States v. Miranda, 248 F.3d 434, 445 *754(5th Cir.2001) (concluding that Apprendi error affects substantial rights); United States v. Wilson, 244 F.3d 1208, 1220 n. 7 (10th Cir.2001) (recognizing that Apprendi error affected substantial rights where sentence exceeded authorized sentence by ten years)). See also United States v. Frazier, 280 F.3d 835, 854-55 (8th Cir.2002) (noting, in plain error case, that defendant’s sentence based on district court’s drug quantity determinations was both plain error and affects substantial rights, but affirming sentence because defendant could not show serious effect on fairness and integrity of proceedings). Conversely, we have found substantial rights unaffected where the resulting sentence would have been the same absent the error. See Diaz, 296 F.3d at 684 (finding substantial rights not violated where the Apprendi error could have been corrected by running the sentences consecutively under the sentencing guidelines); United States v. Sturgis, 238 F.3d 956, 960-61 (8th Cir.2001) (explaining that where the defendant’s sentence would have been the same after recalculation to correct the Apprendi error, the defendant suffered no prejudice).
In other cases, we have looked to whether the record would have rationally permitted a contrary finding on the omitted element, and found the error harmless where the record demonstrated overwhelming and uncontroverted evidence on that issue. See United States v. Wright, 248 F.3d 765, 767 (8th Cir.2001) (per cu-riam) (remanding for resentencing where indictment did not allege serious bodily injury requisite to sentence enhancement but noting that testimony at resentencing “might provide overwhelming evidence ... of serious bodily injury, making the defect in Wright’s indictment harmless error under Jones ”); United States v. Anderson, 236 F.3d 427, 430 (8th Cir.2001) (finding Apprendi error harmless beyond a reasonable doubt where “no rational jury could have found appellants guilty of the substantive offense, yet at the same time found that the amount of [drugs] the conspiracy sought to produce was less than [the amount sufficient to support the court’s sentence].”). Cf. United States v. Steyskal, 38 Fed.Appx. 343 (8th Cir.2001) (per curiam) (unpublished) (vacating enhanced sentence based on Apprendi error where court could not conclude beyond a reasonable doubt that jury would have found the quantities necessary for the higher sentence).
Although there is no doubt that the latter type of analysis is appropriate on harmless error review of a Sixth Amendment challenge, see Neder, 527 U.S. at 5, 119 S.Ct. 1827, a recent Supreme Court decision suggests that it may be less applicable in the Fifth Amendment context. In United States v. Cotton, 535 U.S. 625, 122 S.Ct. 1781, 152 L.Ed.2d 860 (2002), the Court applied plain error review and affirmed a defendant’s enhanced sentence for drug conspiracy under the fairness prong of plain error review even though the indictment failed to allege drug quantity. See id. at 634, 122 S.Ct. 1781. The Court acknowledged the plain error, but held that, given the overwhelming and un-controverted evidence of drug quantity adduced at trial, the defendant could not show that the fairness, integrity, or public reputation of the judicial proceedings was seriously affected — a requisite showing unique to the plain error test. Id.; see also Johnson v. United States, 520 U.S. 461, 470, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997) (where evidence of materiality was “overwhelming” and “essentially uncontro-verted,” defendant could not prove fairness-integrity deficiency essential to discretionary correction under plain error review). Accordingly, the Court expressly left open the question whether an omitted element affects substantial rights. *755Cotton, 535 U.S. at 632-33, 122 S.Ct. 1781.
We nevertheless find Cotton instructive on the issue of substantial rights. If, after Cotton, the fairness-integrity prong of the plain error test looks to the record for overwhelming and/or uncontroverted evidence, it follows that an analysis of whether substantial rights were affected — a separate and presumably independent element of plain error review — cannot turn on precisely the same factors. Thus, Cotton strongly suggests that a determination of whether a defendant’s substantial rights were affected may require — at least in an indictment challenge — something more, or different, than a straightforward review of the record.
Complicating matters further is the fact that the large majority of post-Apprendi appeals involve Sixth Amendment challenges. We recognize that the analyses, and outcomes, in the Sixth Amendment context may not be precisely analogous to Fifth Amendment challenges. And finally, there is the fact that this is a death case. While each side can proffer harmless error case law favorable to its position, the parties have not directed us to, nor have we found, any analogous case law involving capital crimes. As our discussion below demonstrates, our conclusion in this appeal does not hinge on the fact that this case involves the death penalty, but we would be remiss not to recognize the unique circumstances of this case with regard to the effect of the error at issue. See. e.g., Gardner v. Florida, 430 U.S. 349, 357-58, 97 S.Ct. 1197, 51 L.Ed.2d 393 (1977) (“[Djeath is a different kind of punishment from any other which may be imposed in this country. From the point of view of the defendant, it is different in both its severity and its finality. From the point of view of society, the action of the sovereign in taking the life of one of its citizens also differs dramatically from any other legitimate state action.”) (internal citations omitted).
With these principles in mind, we turn to the government’s arguments for harmless error in this case.
2. Application to Allen’s case:
As indicated above, we believe the standard of review is critical to Allen’s appeal. If we were reviewing this case under the plain error standard, we would likely conclude that Allen does not merit relief because the pre-trial notice and petit jury findings appear to have sufficiently guaranteed the fairness, integrity, and public reputation of the judicial proceedings in this case. At issue here, however, is harmless error review which does not include a separate fairness-integrity inquiry. While the reliability and integrity of the proceedings are undoubtedly relevant, a determination that the proceedings were fair does not preclude a finding that Allen’s substantial rights were affected, i.e., that the error prejudicially influenced the outcome of the district court proceedings.
We decline to construe Rule 52(a) in a way which renders harmless all indictment errors in federal capital cases. Nor will we interpret the Fifth Amendment in a manner that would strictly curtail the right to grand jury indictment. The government’s theory would sanction indictment by information in all cases, or at least make such a practice constitutionally harmless error. Further, it would permit the government to indict narrowly and then expand or change the case and charges as it so chose — as long as it informed the defendant as it went along. To use an extreme example, a defendant could be indicted on a simple weapons charge, and then tried and convicted on completely unrelated drug charges, and the error would be harmless if the defendant re*756ceived notice of the government’s intention prior to trial. We presume that if a defendant challenged such practices prior to trial, he would succeed and the government would be directed to obtain an indictment on each charged offense. However, there will be instances where errors occur or objections are not timely made. If, as the government’s theory posits, a defendant’s substantial rights are not affected by practices such as these, it is difficult to imagine any scenario by which a defendant could ever prevail in an Indictment Clause challenge that, for whatever reason, was not resolved in his favor prior to trial. We find nothing in the underpinnings of the Indictment Clause, or in Supreme Court case law, that suggests that such an approach would be constitutional. See, e.g., Smith v. United States, 360 U.S. 1, 9, 79 S.Ct. 991, 3 L.Ed.2d 1041 (1959) (re versing federal kidnapping conviction initiated by information, and stating that “[t]he Fifth Amendment made the [grand jury indictment] rule mandatory in federal prosecutions in recognition of the fact that the intervention of a grand jury was a substantial safeguard against oppressive and arbitrary proceedings ... [T]o permit the use of informations where ... the charge states a capital offense, would ... make vulnerable to summary treatment those accused of ... our most serious crimes.”) (internal citation omitted).
We note that if Allen’s trial were still pending, there is virtually no doubt that the government would seek a superseding indictment which included the statutory aggravating factors referenced in the notice of intent to seek the death penalty. See United States v. Pennington, No. 3:01-CR-35-R, slip op. at 3 (W.D.Ky. Feb. 21.2003) (granting defendant’s motion to preclude imposition of- the death penalty where indictment did not allege death-qualifying statutory aggravating factor or requisite mens rea, and government did not seek superseding indictment prior to jeopardy attaching “notwithstanding the acknowledged mandate from, the Attorney General to seek a superseding indictment in all pending federal death penalty cases so as to include the requisite intent and statutory aggravators”); United States v. Regan, 221 F.Supp.2d 672, 675 (E.D.Va.2002) (noting that, in light of Ring, the government filed a second superseding indictment re-alleging espionage charges and including the statutory aggravating factors previously set forth only in the notice of intent to seek the death penalty). We recognize that at the time of Allen’s indictment, Walton was still good law, and thus the indictment appeared constitutionally sufficient.8 But there is no good-faith exception to a violation of a properly asserted right to indictment by grand jury, and we now know that Allen’s indictment was constitutionally deficient — that, in fact, Allen was correct back in 1997 when he challenged the indictment before the trial court and in 2000 when he challenged it on appeal.
Allen was constitutionally entitled to a separate and independent determination by a grand jury that probable cause existed to find the death-qualifying facts in this case. As a result of the error, Allen was denied the first of a constitutionally-mandated two-tiered check on prosecutorial power — a protection which reaches paramount importance in a capital case. Consequently, the death sentence imposed exceeded that authorized by the indicted offense and was based solely on post-grand jury charging decisions. See Stirone, 361 U.S. at 218, 80 S.Ct. 270 *757(“The very purpose of the requirement that a man be indicted by grand jury is to limit his jeopardy to offenses charged by a group of his fellow citizens acting independently of either prosecuting attorney or judge.”) (emphasis added).
The government points to the practical reality of grand jury practice, specifically the low burden of proof and majority vote required to obtain a grand jury indictment, and the rarity of a grand jury refusing a prosecutor’s requested charge. The problem with this speculative reasoning for our purposes, however, is that it disregards the constitutional framework that, for felonies and capital crimes, places two separate bodies of citizens between the accused and a state-sanctioned judgment. In this respect, we see an arguable distinction between a Sixth Amendment challenge to judge-made findings and a Fifth Amendment indictment clause challenge. As observed by the Supreme Court:
If it lies within the province of a court to change the charging part of an indictment to suit its own notions of what it ought to have been, or what the grand jury would probably have made it if their attention had been called to suggested changes, the great importance which the common law attaches to an indictment by a grand jury, as a prerequisite to a prisoner’s trial for a crime, and without which the constitution says ‘no person shall be held to answer,’ may be frittered away until its value is almost destroyed.
Ex parte Bain, 121 U.S. 1, 10, 7 S.Ct. 781, 30 L.Ed. 849 (1887), quoted in Stirone, 361 U.S. at 217, 80 S.Ct. 270. See also Cotton, 535 U.S. at 631, 634, 122 S.Ct. 1781 (citing Bain, 121 U.S. 1, 7 S.Ct. 781, 30 L.Ed. 849, Stirone, 361 U.S. 212, 80 S.Ct. 270, 4 L.Ed.2d 252, and Russell v. United States, 369 U.S. 749, 82 S.Ct. 1038, 8 L.Ed.2d 240 (1962), for the “settled proposition of law” that “an indictment may not be amended except by resubmission to the grand jury, unless the change is merely a matter of form,” and approving the general proposition that “the Fifth Amendment grand jury right serves a vital function in providing for a body of citizens that acts as a check on prosecutorial power”); United States v. Miller, 471 U.S. 130, 142-43 & n. 7, 105 S.Ct. 1811, 85 L.Ed.2d 99 (1985) (noting the Court’s consistent reaffirmation of Bain as standing for recognition of the important constitutional safeguard represented by the grand jury). See also Harris v. United States, 536 U.S. 545, 564, 122 S.Ct. 2406, 153 L.Ed.2d 524 (2002) (Kennedy, J., concurring) (“The grand and petit juries thus form a ‘strong and twofold barrier ... between the liberties of the people and the prerogative of the [government].’ ”) (quoting Duncan v. Louisiana, 391 U.S. 145, 151, 88 S.Ct. 1444, 20 L.Ed.2d 491 (1968)).
There may be instances where a reviewing court can confidently say that given the grand jury’s findings, that same grand jury would have found the omitted element had the prosecutor asked. See, e.g., Cotton, 535 U.S. at 633, 122 S.Ct. 1781 (noting, under fairness-integrity prong of plain error review, that “[s]urely the grand jury, having found that the conspiracy existed, would have also found that the conspiracy involved at least 50 grams of cocaine base”). Here, however, the government asks us to determine what the grand jury would have found based on the petit jury’s findings. The reasoning underlying the Supreme Court’s comment in Cotton, and some of our Sixth Amendment Apprendi decisions, does not hold in the context of this case. Nothing in the petit jury’s findings compels the conclusion that a completely different group of people — the grand jury — would have found the same fact, even if the evidentiary burdens are lower. This is particularly true where, as here, at issue are relatively qualitative de*758terminations which do not lend themselves to precise fact-finding in the same way that drug quantity determinations might. See, e.g., State v. Finch, 137 Wash.2d 792, 975 P.2d 967, 1007-08, cert. denied, 528 U.S. 922, 120 S.Ct. 285, 145 L.Ed.2d 239 (1999) (finding that there is no such thing as “overwhelming evidence” of the death penalty because although there can be objective evidence of a person’s guilt or evidence, such that a reviewing court can say whether a trial jury’s deliberations would have come out the same way as to the underlying offense, aggravating and mitigating factors are “of a more subjective nature ...”).
Because we are unable to conclude beyond a reasonable doubt that the indictment error did not affect Allen’s substantial rights, the government has not met its burden to prove that the error was harmless. See Neder, 527 U.S. at 19, 119 S.Ct. 1827 (cautioning that if, after thorough examination of the record, a reviewing court cannot conclude beyond a reasonable doubt that the error did not prejudicially influence the outcome, the court should not find the error harmless). Accordingly, we vacate Allen’s death sentence and remand to the district court for imposition of a life sentence.
. The parties briefed two other post-Ring issues as well: (1) whether the mens rea element required under 18 U.S.C. § 3591(a)(2) is essential to, and missing from, the indictment; and (2) whether the Federal Death Penalty Act is unconstitutional because it does not require participation of the grand jury in the charging of aggravating circumstances in a capital case. Because our conclusion with regard to the statutory aggravator issue is dispositive of Allen's appeal, we need not reach these other issues.
. Because Apprendi involved a state crime, the Fifth Amendment right to indictment by a grand jury was not at issue, as that right has *749not been incorporated into to the Fourteenth Amendment. See Apprendi, 530 U.S. at 477 n. 3, 120 S.Ct. 2348 (expressly leaving open the indictment issue).
. Under § 3592(c)(1), entitled "[djeath during commission of another crime,” a statutory aggravating factor is established if a "death or injury resulting in death occurred during the commission or attempted commission of, or during the immediate flight from the commission of, an offense under” one of twenty code sections, ranging from destruction of aircraft or aircraft facilities to kidnapping or hostage taking to treason. See Jackson, 327 F.3d at 303-04 (rejecting post-Ring challenge to indictment in death case where the indictment clearly charged the defendant with the fact that death occurred during the commission of a kidnapping, an enumerated offense under § 3592(c)(1)).
. “[A] constructive amendment occurs where proof at trial goes beyond the parameters of the indictment in that it establishes offenses different from or in addition to those charged by the grand jury,” United States v. Jefferson, 334 F.3d 670, 673 (7th Cir.2003) (quotation omitted). See also United States v. Johnson, 934 F.2d 936, 941 (8th Cir.1991) ("Constructive amendments occur when the terms of the indictment are altered in effect by either the admission of evidence or the use of jury instructions which modify the essential elements of the offense charged so that a substantial likelihood exists that the defendant was convicted of an offense other than that charged in the indictment.”).
. By contrast, where a defendant does not object at trial, a court may grant discretionary relief only if the defendant can prove that plain error occurred, that the error affected his substantial rights, and that the error "seriously affected the fairness, integrity, or public reputation of judicial proceedings.” United States v. Diaz, 296 F.3d 680, 683 (8th Cir.2002) (citing Cotton, 535 U.S. 625, 122 S.Ct. 1781). See also Fed.R.Crim.P. 52(b). It is undisputed that Allen properly preserved his constitutional claim.
. In Olano, the defendant did not object at the trial level and the Court reviewed his challenge for plain error. Olano, 507 U.S. at 730, 113 S.Ct. 1770. Although the plain and harmless error tests differ in significant ways, both require that the error affect a defendant's substantial rights, and the parties have provided no authority to suggest that the analysis of when substantial rights are affected is distinguishable in the plain and harmless error cases. Cf. id. at 734, 113 S.Ct. 1770 (noting identical language in subsections (a) and (b) of Rule 52, and citing both harmless and plain error cases in support of Olano’s articulation of the standard).
. We note, however, that nothing precluded the government from seeking a prophylactic superseding indictment after Allen challenged the sufficiency of the indictment in pretrial proceedings.