
593 F.3d 547 (2010)
Joseph E. CORCORAN, Petitioner-Appellee, Cross-Appellant,
v.
Mark LEVENHAGEN, Superintendent, Respondent-Appellant, Cross-Appellee.
Nos. 07-2093, 07-2182.
United States Court of Appeals, Seventh Circuit.
Submitted December 14, 2009.
Decided January 27, 2010.
*549 Alan M. Freedman (submitted), Midwest Center for Justice, Evanston, IL, Laurence E. Komp (submitted), Manchester, MO, for Petitioner-Appellee.
James B. Martin (submitted), Office of the Attorney General, Indianapolis, IN, for Respondent-Appellant.
Before BAUER, WILLIAMS and SYKES, Circuit Judges.
BAUER, Circuit Judge.
Joseph Corcoran murdered four people, and an Indiana court sentenced him to death. The district court granted habeas relief on Corcoran's Sixth Amendment claim. We reversed on the Sixth Amendment issue, Corcoran v. Buss, 551 F.3d 703 (7th Cir.2008), but as the Supreme Court explained, we improperly omitted discussion of Corcoran's other habeas challenges. Corcoran v. Levenhagen, ___ U.S. ___, 130 S.Ct. 8, 9, 175 L.Ed.2d 1 (2009). We include that discussion here, after a full and fresh look at the record. We find that all of Corcoran's remaining habeas challenges are waived, and that three of them are frivolous, but that one of the challenges nevertheless entitles him to a new sentencing hearing.

I. BACKGROUND
We assume familiarity with the facts surrounding Joseph Corcoran's murders and the path Corcoran traversed through the state and federal court systems, all of which we recounted in our prior decision. See Corcoran, 551 F.3d at 704-08. That decision found that Corcoran's death sentence did not violate his jury trial rights *550 under the Sixth Amendment, and that Corcoran was competent to waive state post-conviction proceedings. Id. at 712, 714. But the decision omitted discussion of four other challenges that Corcoran raised in the district court, that the district court failed to address, and that Corcoran did not appeal in this court although he was a cross-having cross-appealed a separate challenge. Those four challenges, which the Supreme Court advises us to either address ourselves or remand for the district court to consider, are that: (1) the Indiana trial court improperly considered non-statutory aggravating circumstances and failed to consider six mitigating circumstances; (2) Indiana's capital sentencing statute was unconstitutional; (3) the prosecution committed misconduct in the closing argument to the sentencing jury; and (4) Corcoran should not be executed because he suffers from a mental illness. Corcoran, 130 S.Ct. at 9; see Habeas Pet. at 10-13, 14-15.

II. DISCUSSION
A preliminary issue on remand from the Supreme Court, and the only issue that Corcoran addresses under Circuit Rule 54, as his "position as to the action which ought to be taken by this court on remand," is whether we should address his remaining habeas challenges ourselves or remand to the district court.
The Supreme Court explicitly gave us a choice. See Corcoran, 130 S.Ct. at 9 ("The Seventh Circuit should have permitted the District Court to consider Corcoran's unresolved challenges to his death sentence on remand, or should have itself explained why such consideration was unnecessary."); cf. Cone v. Bell, ___ U.S. ___, 129 S.Ct. 1769, 1786, 173 L.Ed.2d 701 (2009) (ordering a remand to the district court). Sometimes we have chosen, after reversing a district court's grant of habeas relief, to address remaining habeas challenges not addressed by the district court ourselves, Sprosty v. Buchler, 79 F.3d 635, 645 (7th Cir.1996), and sometimes we have remanded. Stewart v. Peters, 958 F.2d 1379, 1388 (7th Cir.1992); Clark v. Duckworth, 906 F.2d 1174, 1179 (7th Cir.1990). The decision whether to remand in these circumstances is discretionary. See Corcoran, 130 S.Ct. at 9; Singleton v. Wulff, 428 U.S. 106, 121, 96 S.Ct. 2868, 49 L.Ed.2d 826 (1976) ("The matter of what questions may be taken up and resolved for the first time on appeal is one left primarily to the discretion of the courts of appeals, to be exercised on the facts of individual cases.").
We exercise our discretion here to decide the merits ourselves, because Corcoran's remaining challenges are rudimentary to the point of requiring no additional briefing, we are equally positioned with the district court to reach a disposition based on a full review of the present state court record, and a review by the district court would at any rate be subject to our review de novo. See Cone, 129 S.Ct. at 1792 (Alito, J., concurring in part and dissenting in part); Lonchar v. Thomas, 517 U.S. 314, 320, 116 S.Ct. 1293, 134 L.Ed.2d 440 (1996) (noting that appellate courts may "expedite proceedings on the merits"); Circuit Rule 22(d)(3) ("The merits of an appeal may be decided summarily if the panel decides that an appeal is frivolous."). In short, a remand to the district court is "unnecessary." Corcoran, 130 S.Ct. at 9.
Nor do we lack jurisdiction to rule on the merits. We have jurisdiction to take an appeal from the district court's decision  granting habeas relief on less than all the claims in Corcoran's multi-claim petition without adjudicating the remaining claims seeking the same relief  because it was a "final order." 28 U.S.C. § 2253. See, e.g., Sprosty v. Buchler, 79 *551 F.3d 635, 645 (7th Cir.1996) (collecting cases). It matters not that a certificate of appealability was granted in this case, Corcoran v. Buss, No. 3:05-CV-389 (N.D.Ind. May 17, 2007), but not with respect to the remaining claims. See Owens v. Boyd, 235 F.3d 356, 358 (7th Cir.2001) ("[A] defect in a certificate of appealability is not a jurisdictional flaw.").
So we proceed with the merits of Corcoran's additional habeas challenges. Arguments not raised on appeal or cross-appeal are waived. See Fed. R.App. P. 28.1(c)(2); United States v. Johnson, 335 F.3d 589, 592 (7th Cir.2003); United States v. Berkowitz, 927 F.2d 1376, 1391 (7th Cir.1991); Sanchez v. Miller, 792 F.2d 694, 703 (7th Cir.1986). Corcoran as cross-appellant failed to appeal the four claims and thus he waived them.
Nevertheless, we may consider Corcoran's challenges for plain error, because "in exceptional circumstances, appellate courts, in the public interest, may, of their own motion, notice errors to which no exception has been taken, if the errors are obvious, or if they seriously affect the fairness, integrity, or public reputation of judicial proceedings." United States v. Atkinson, 297 U.S. 157, 160, 56 S.Ct. 391, 80 L.Ed. 555 (1936). For most of Corcoran's challenges we find no plain error, so we need not decide whether they present exceptional circumstances. But for one challenge, which we discuss first, we think that the state trial court's decision resulted in two obviously unreasonable fact determinations entitling Corcoran to a new sentencing hearing.

A. Sentencing Process
Corcoran claimed that the Indiana trial court considered non-statutory aggravating circumstances,  i.e., Corcoran's future dangerousness, his victims' innocence, and the murders' heinousness  in contravention of state law. See Bivins v. State, 642 N.E.2d 928, 955-56 (Ind.1994) (outlawing the use of non-statutory aggravating circumstances under Indiana state law). The trial court disagreed, stating that "in balancing the proved aggravators and mitigators, [the trial court] emphasizes ... that it only relied upon those proven statutory aggravators." See Corcoran v. State, 774 N.E.2d 495, 498 (Ind.2002) (quoting the trial court).
But this finding of fact, that the trial court did not consider non-statutory aggravators in the balancing process used to determine Corcoran's death sentence, was obviously in error, if we are to believe what the trial court added next. Specifically, it stated that its "remarks at the sentencing hearing, and the language in the original sentencing order,"  both regarding the use of the three non-statutory aggravators about which Corcoran complained  "explain why such high weight was given to the statutory aggravator of multiple murder." See id. (emphasis added). In other words, the court added weight to a statutory aggravator based on the non-statutory aggravators. And factor weighting is part of factor "balancing," the very process in which the trial court disclaimed reliance on non-statutory aggravators. So unlike the Indiana Supreme Court, we are far from "satisfied that the trial court has relied only on aggravators listed in Indiana Code § 35-50-2-9(b)." Corcoran v. State, 774 N.E.2d 495, 499 (Ind.2002). Indeed, we find this an "unreasonable determination of the facts" in light of the trial court's proceedings, thus warranting habeas relief. 28 U.S.C. § 2254.
Nothing in this opinion prevents Indiana from adopting a rule, contra Bivins, 642 N.E.2d at 955-56, permitting the use of non-statutory aggravators in the death sentence selection process. See Zant v. *552 Stephens, 462 U.S. 862, 878, 103 S.Ct. 2733, 77 L.Ed.2d 235 (1983) (permitting their use under federal law). But the state trial court must reconsider its sentencing determination, and this time may not find, contrary to logic, that it both did and did not consider non-statutory aggravating circumstances when it sentenced Corcoran to death.
Also, the trial court should address Corcoran's age (at the time of the murders, he was twenty-two) as a mitigating factor in order to cure a different fact-finding error by the Indiana Supreme Court. Corcoran claimed that the Indiana trial court failed to consider six of the ten mitigating circumstances Corcoran proffered: (1) his age; (2) his substantially impaired ability to appreciate the criminality of his conduct or to conform that conduct with the requirements of the law; (3) his inability to competently assist in his defense; (4) his forethought to protect his seven-year-old niece during the murders; (5) his good behavior in jail before sentencing; and (6) his admission of guilt "at all stages of the legal process" including the trial. When the trial court first sentenced Corcoran, it explicitly discussed and rejected the last five of these mitigators  but not Corcoran's age  as either false or non-mitigatory. State of Indiana v. Corcoran, No. 02D04-9707-CF-465, at 3-6, 1999 WL 34856148 (Ind.Super. Aug. 26, 1999). When the Indiana Supreme Court later advised it to clarify only whether it had used non-statutory aggravators, it is unsurprising that the trial court declined to reiterate its analysis of the five mitigators it had previously rejected. But at no time did the trial court offer an explanation for rejecting Corcoran's age as non-mitigatory, as was required by Indiana law. See Corcoran, 774 N.E.2d at 501 (requiring the trial court to "list specific facts and reasons that led the court to finding [mitigating circumstances'] existence"). Thus, the Indiana Supreme Court's finding of fact, that the trial court "analyzed" and "rejected" Corcoran's age in its sentencing order, id. at 500, was obviously in error, because the sentencing order makes no mention of Corcoran's age except to note that Corcoran proffered it as a mitigator.
Nor did the Indiana Supreme Court cure this oversight by itself evaluating Corcoran's age as a mitigator. See Clemons v. Mississippi, 494 U.S. 738, 748-49, 110 S.Ct. 1441, 108 L.Ed.2d 725 (1990) (finding that a state appellate court satisfies the constitutional requirement of an individualized and reliable sentencing determination in capital cases by itself weighing aggravating and mitigating circumstances). In weighing and rejecting Corcoran's age as non-mitigatory, the Indiana Supreme Court found dispositive that "Corcoran [was] well past the age of sixteen where the law requires special treatment" and thus that the trial court had not "abuse[d] [its] discretion." Corcoran, 774 N.E.2d at 500; cf. Roper v. Simmons, 543 U.S. 551, 125 S.Ct. 1183, 161 L.Ed.2d 1 (2005) (raising the minimum death-eligible age to eighteen). But as we discussed above, the trial court had not exercised any "discretion." Rather, it had failed altogether to intimate any consideration of Corcoran's age. Thus, in erroneously finding once again that the trial court had exercised its discretion, the Indiana Supreme Court weighted Corcoran's age under an abuse-of-discretion standard, rather than the more searching standard required under Indiana law. See Monegan v. State, 756 N.E.2d 499, 504 (Ind.2001) ("Focusing on chronological age, while often a shorthand for measuring culpability, is frequently not the end of the inquiry for people in their teens and early twenties.... There are both relatively old offenders who seem clueless and relatively *553 young ones who appear hard and purposeful.").
Again, nothing in this opinion prevents Indiana from adopting a rule, contra Corcoran, 774 N.E.2d at 501, permitting a court to take account of mitigating factors that have been properly admitted into evidence, without explicitly discussing its consideration of those factors on the record. See, e.g., Penry v. Johnson, 532 U.S. 782, 797, 121 S.Ct. 1910, 150 L.Ed.2d 9 (2001) (requiring only that the sentencer be able to give adequate mitigating effect to mitigating evidence). And nothing in this opinion prevents Indiana from finding Corcoran's age irrelevant to selecting his death sentence. See Roper, 543 U.S. 551, 125 S.Ct. 1183, 161 L.Ed.2d 1. But as the state trial court conducts its new sentencing hearing, to rectify the fact-finding error with respect to non-statutory aggravators discussed above, it should also discuss whether it finds Corcoran's age to be a mitigating circumstance. This will prevent non-compliance with Indiana law, and  more pertinent to our inquiry on federal habeas review  cure the Indiana Supreme Court's "unreasonable determination of the facts" in light of the trial court's proceedings. 28 U.S.C. § 2254.

B. Indiana's Capital Sentencing Statute
At this point, we could remand to the district court with instructions to grant Corcoran's habeas petition, and call it a day. But that would allow Corcoran's remaining habeas challenges to continue languishing unadjudicated, a scenario we have cautioned against. Indeed, we have advised that "the better practice in habeas corpus death cases is for the judge to rule on all the grounds presented in the petition." Stewart, 958 F.2d at 1388.
So we proceed with Corcoran's next claim, that Indiana's capital sentencing statute was unconstitutional under the Eighth Amendment's prohibition on cruel and unusual punishment and the Fourteenth Amendment's guarantee of due process, because the statute's factors for determining whether one is eligible for the death penalty "subject a defendant to life without parole or death," thus providing "no guidance to differentiate between life or death." Habeas Pet. at 11-12. The statute at the time of Corcoran's sentence provided, and now also provides, that a defendant "may be sentenced to (1) death; or (2) life imprisonment without parole," if the state "prove[s] beyond a reasonable doubt the existence of at least one ... aggravating circumstance[]." Ind.Code. §§ 35-50-2-3, 9 (1993). Because the eligibility factors subject a defendant to either death or life imprisonment without parole, Corcoran argued, "the Indiana legislature is equating the penological purposes between the two penalties," thus failing to provide "constitutionally required narrowing." Habeas Pet. at 11.
It is true that death penalty statutes must adequately narrow the class of persons eligible for death. Thus, the Supreme Court has invalidated statutes providing juries with untrammeled discretion to impose the death penalty, Furman v. Georgia, 408 U.S. 238, 92 S.Ct. 2726, 33 L.Ed.2d 346 (1972), or guiding juries' discretion with overly vague aggravating circumstances. Godfrey v. Georgia, 446 U.S. 420, 100 S.Ct. 1759, 64 L.Ed.2d 398 (1980). But Corcoran made no challenge to the existence or nature of the then thirteen aggravating circumstances used to narrow the class of persons eligible for death. Rather, he challenged only that the existence of at least one of those circumstances made him eligible not only for death, but also for life without parole. It matters not whether the statute says that a defendant may be sentenced to "death or *554 life imprisonment without parole," as the statute reads, or simply "death," as Corcoran would have it. In both cases, the door has been opened so that a defendant may be sentenced to either. Thus, Corcoran's eligibility challenge lacks merit, because the semantic changes he would make to the statute's language on eligibility would have no effect on its meaning.
Nor does it matter that death and life without parole are "dueling options" for selection once a defendant is found eligible. Habeas Pet. at 11-12. The Indiana statute provides that a jury may impose either death or life without parole upon finding (1) an aggravating circumstance, and (2) that aggravating circumstances outweigh any mitigating circumstances. Ind.Code §§ 35-50-2-9(e), (l). In other words, the statute guides the jury in imposing death or life without parole, but it affords no guidance on how to choose between the two. But these "dueling options" are not the sort of "untrammeled discretion to impose or withhold the death penalty" that the Constitution prohibits. Gregg v. Georgia, 428 U.S. 153, 195 n. 47, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976) (citing Furman, 408 U.S. 238, 92 S.Ct. 2726, 33 L.Ed.2d 346). Rather, the Supreme Court upheld in Gregg a scheme where the jury, as an alternative to death, "may fix the penalty at life imprisonment, if you see fit to do so, for any reason satisfactory to you or without any reason." Ga. Suggested Pattern Jury Instruction 2.15.50 (2009) (cited as existing when Gregg was decided in Linda E. Carter, Ellen S. Kreitzberg, and Scott W. Howe, Understanding Capital Punishment Law 155 (2d ed.2008)). In sum, "the isolated decision of a jury to afford mercy does not render unconstitutional death sentences imposed on defendants who were sentenced under a system that does not create a substantial risk of arbitrariness or caprice." Gregg, 428 U.S. at 203, 96 S.Ct. 2909.
Corcoran also claimed that the statute is unconstitutional because it "informs the jury that a death sentence acts as an act of mercy in comparison to the life without parole sentence." Habeas Pet. at 12. But the statute does no such thing. Rather, as Corcoran admits, the statute offers "no guidance to differentiate between life or death" once a defendant is found eligible, id., which as discussed above is constitutional under Gregg.
Finally, Corcoran argues that the statute "penalizes individuals for presenting mitigation." Id. Again, the statute does no such thing. Rather, it encourages defendants to present mitigating circumstances, because if enough of them outweigh the aggravating circumstances then a jury is barred from sentencing a defendant to death or life without parole. Ind.Code §§ 35-50-2-9(e), (l).

C. Prosecution's Closing Argument at Sentencing
Corcoran further claimed that he was deprived of due process when the prosecutor made five statements to the sentencing jury at closing argument. One statement, according to Corcoran, improperly "speculat[ed] on what a victim imagined or said: `[W]e imagine that last victim must gasp for breath, must grasp for mercy.'" Habeas Pet. at 12. Another statement "speculated on future dangerousness and misdefined life without parole in stating `[Corcoran] is not a man we want back on our streets in his lifetime.'" Id. Two others "speculated on victim opinion as to the appropriate sentence[:]
I can hear all four of them, Jim, Scott, Tim, and Doug[;] their souls, their very life blood spilled in that home cries out for equality, justice. And you know we can never fully give those men that equality of justice and do you know *555 why? Because this man has only one life to give for the four he took.... I think I can still hear Jim and Tim and Doug and Scott and you know what; they don't ask us for revenge, they ask again for the equality of justice and that equality of justice comes with retribution."
Id. at 12-13. And the fifth statement "describe[d] Petitioner as a dangerous individual who placed all people in danger including the jury: Innocent lives are expendable. All of us." Id. at 13.
These arguments about the prosecution's closing argument are waived for the additional reason that Corcoran never raised them in state court. See Corcoran v. State, 739 N.E.2d 649, 655 (Ind.2000). By raising the argument for the first time with the district court, Corcoran procedurally defaulted his claim. See 28 U.S.C. § 2264.
Corcoran points to no cause for this procedural default, so we will not grant habeas relief unless the prosecutor's arguments resulted in "a fundamental miscarriage of justice." Sawyer v. Whitley, 505 U.S. 333, 339, 112 S.Ct. 2514, 120 L.Ed.2d 269 (1992). We find no miscarriage of justice here, as the prosecutor's statements are not the type of constitutional error that would render Corcoran ineligible for the death penalty. Id. at 341, 347, 112 S.Ct. 2514.

D. Incompetence To Be Executed
Finally, Corcoran claimed he should not be executed because he suffers from a mental illness. Indeed, the Constitution prohibits the execution of a prisoner who is insane. Ford v. Wainwright, 477 U.S. 399, 410, 106 S.Ct. 2595, 91 L.Ed.2d 335 (1986); see also Panetti v. Quarterman, 551 U.S. 930, 127 S.Ct. 2842, 168 L.Ed.2d 662 (2007). But Corcoran must raise the argument of his incompetence to be executed in Indiana's state courts before he can do so here. 28 U.S.C. § 2254(b)(1). Indeed, Corcoran made no claim that Indiana lacks an effective process to comply with Ford v. Wainwright. To the contrary, Indiana permits additional post-conviction review on Ford claims "after the usual channels of appeal have been exhausted." Baird v. State, 833 N.E.2d 28, 29 (Ind.2005); see also Ind. Post-Conviction Rule 1(12) (allowing a successive habeas petition "if the petitioner establishes a reasonable probability that the petitioner is entitled to post-conviction relief"). Therefore, his Ford claim is unripe.

III. CONCLUSION
The habeas claims actually before this court are meritless, as we previously found in Corcoran, 551 F.3d 703. The claims Corcoran declined to pursue in this court are waived, and three of them are anyway meritless or unripe. But Corcoran's challenge to the state trial court's sentencing process has obvious merit, for the reasons discussed above. Therefore, we AFFIRM the district court's conditional grant of Corcoran's petition for a writ of habeas corpus, but we modify its order to grant the writ unless within 120 days the state court holds a new sentencing hearing in accordance with this opinion.
