PER CURIAM.

This habeas case returns to us from the Supreme Court for a second time. See Wilson v. Corcoran, ___ U.S. ___, 131 S.Ct. 13, 178 L.Ed.2d 276 (2010); Corcoran v. Levenhagen, ___ U.S. ___, 130 S.Ct. 8, 175 L.Ed.2d 1 (2009). Joseph Corcoran's capital case has a complex history in state and federal court, which we set forth more completely in our two prior opinions, see Corcoran v. Levenhagen, 593 F.3d 547 (7th Cir. 2010), and Corcoran v. Buss, 551 F.3d 703 (7th Cir. 2008), and will repeat here only as necessary to correct the mistakes the Supreme Court has identified and get the case back on track.

In 1997 Joseph Corcoran shot and killed four men. An Indiana jury convicted him of four counts of murder and recommended a sentence of death. The state trial court agreed and imposed the death penalty. On direct appeal Corcoran raised several challenges to his sentence. The Indiana Supreme Court rejected most of these arguments, but vacated the sentence after finding that the trial court might have violated Indiana law by weighing non-statutory aggravating factors when deciding whether to impose the death penalty. See Corcoran v. State, 739 N.E.2d 649, 657-58 (Ind. 2000). On remand the state trial court re-imposed the death sentence with an explanatory order, and the Indiana Supreme Court affirmed. Corcoran v. State, 774 N.E.2d 495, 498-99 (Ind. 2002). Corcoran waived state post-conviction relief after the trial court found him competent to forego further challenges to his sentence; the Indiana Supreme Court affirmed this determination as well. Corcoran v. Buss, 551 F.3d at 706. He later changed his mind and tried to file a petition for post-conviction relief. The trial court dismissed the petition as untimely, and the Indiana Supreme Court affirmed. Id., at 707.

The case then moved to federal court. Corcoran filed a habeas petition in the United States District Court for the Northern District of Indiana raising multiple claims. But he vacillated again and made an effort to withdraw this petition. Id. The district court rejected this attempt and eventually considered two of Corcoran's claims for relief. The court held that (1) the Indiana courts had reasonably concluded that Corcoran was competent to waive his state post-conviction remedies; and (2) the prosecutor violated the Sixth Amendment by offering to forego the death penalty if Corcoran would waive his right to a jury trial. The court granted habeas relief on the Sixth Amendment claim, finding that the state supreme court's contrary holding on this issue violated United States v. Jackson, 390 U.S. 570, 88 S.Ct. 1209, 20 L.Ed.2d 138 (1968). Having granted Corcoran's habeas petition on this ground, the court ordered Indiana to resentence Corcoran to a sentence other than death and did not address any of his remaining claims. Corcoran v. Buss, 551 F.3d at 707-08.

Indiana appealed the district court's order granting the writ of habeas corpus. Corcoran cross-appealed, challenging the court's rejection of his argument about his competence to waive state post-conviction remedies. We reversed the district court's order granting habeas relief on the basis of a Sixth Amendment violation and affirmed on the issue of Corcoran's competence to waive his right to pursue post-conviction remedies. Id. at 709-14. Judge Williams dissented, but only on the competency issue. at 714-18 (Williams, J., dissenting). We remanded "with instructions to deny the writ," id. at 714, overlooking the fact that Corcoran had raised additional claims for relief that the district court had not addressed. This oversight was the subject of the Supreme Court's first decision. The Court granted Corcoran's certiorari petition, vacated our judgment, and remanded for further proceedings, noting that 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." Corcoran v. Levenhagen, 130 S.Ct. at 9.

On remand we made two critical misjudgments — one procedural, one substantive. The procedural mistake was our decision to take up Corcoran's remaining challenges ourselves, without further appellate briefing, rather than sending the case back to the district court so the previously unaddressed claims could be fully adjudicated there. This procedural mis-step led to a substantive error, which the Supreme Court identified in its second decision. Although we rejected most of Corcoran's remaining claims for relief, we ordered the issuance of a habeas writ based on what we said was a violation of Indiana's death-sentencing law, without finding that this error of state law amounted to a violation of a federal right. Corcoran v. Levenhagen, 593 F.3d at 551-52, 555. The Supreme Court reminded us that "[f]ederal courts may not issue writs of habeas corpus to state prisoners whose confinement does not violate federal law." Wilson v. Corcoran, 131 S.Ct. at 14; see also Estelle v. McGuire, 502 U.S. 62, 67-68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991) ("[I]t is not the province of a federal habeas court to reexamine state-court determinations on state-law questions."), and id. at 75, 112 S.Ct. 475 (noting that a state-law evidentiary or instructional error may be grounds for federal habeas relief only if the error "so infused the trial with unfairness as to deny due process of law" (internal quotation marks omitted)). The Court again granted certiorari, vacated our judgment, and remanded for further proceedings, expressing "no view about the merits of the habeas petition." Wilson v. Corcoran, 131 S.Ct. at 17.

In hindsight we should have returned the case to the district court after the first remand from the Supreme Court. We do so now. This will permit the parties to fully air Corcoran's remaining habeas claims and allow the district court to address them in the first instance. We note, however, that neither of the Supreme Court's decisions casts doubt on our resolution of the issues raised in the initial appeal, in which we found no basis for habeas relief on the claimed Sixth Amendment violation or on the issue of Corcoran's competency to waive post-conviction remedies. In his Circuit Rule 54 statement, Corcoran addresses only his remaining claims, not these two; he asks for a remand so that the district court can adjudicate the previously unaddressed grounds for habeas relief.

Accordingly, we REINSTATE and incorporate by reference our earlier opinion in Corcoran v. Buss, 551 F.3d 703, to the extent that it (1) reversed the district court's judgment granting habeas relief on the basis of the claimed Sixth Amendment violation; and (2) affirmed the district court's conclusion that the Indiana courts did not mishandle the issue of Corcoran's competence to waive post-conviction remedies. As we have noted, Judge Williams joined the panel in rejecting Corcoran's Sixth Amendment claim but filed a dissent on the competency issue, see id. at 714-18, which we also reinstate and incorporate herein by reference. We REMAND the case to the district court to permit it to address Corcoran's remaining grounds for habeas relief.