. Chijioke Ben-Yisrayl is an Indiana prisoner serving a 60-year sentence for murder. He appeals from the district court’s denial of his petition for habeas ∗ The Honorable Sharon Johnson Coleman of the Northern District of Illinois, sitting by designation.

relief under 28 U.S.C. § 2254. Although he raised multiple claims in his petition, his sole argument on appeal is that his resentencing counsel was constitutionally ineffective for failing to introduce “a veritable mountain of mitigation evidence.” But he never raised this claim in his habeas petition, and his failure to do so is a waiver. We affirm the judgment.

I. Background

Ben-Yisrayl is well acquainted with the judicial system. In 1984 he was convicted in Indiana state court of capital murder, rape, criminal confinement, and burglary. ^[1] The jury was unable to reach a decision in the penalty phase of trial, so the judge imposed a sentence of death. In case that sen- tence did not hold up on appeal, the judge imposed an alternative sentence of 60 years. On the remaining counts, the judge imposed an aggregate term of 90 years.

The case bounced back and forth for many years in the state trial and appellate courts as the death sentence and other issues were litigated on direct review and in post- conviction proceedings. Prosecutors eventually withdrew their request for the death penalty and settled for the alter- native 60-year sentence on the murder conviction. Ben-Yisrayl won a reversal of that sentence as well. On resentencing the trial judge reimposed the 60-year sentence, and this time it was affirmed. Post-conviction proceedings on other issues continued.

In the meantime, Ben-Yisrayl pursued habeas relief in federal court under § 2254. Because he had yet to complete state post-conviction review, the district judge stayed the proceedings. When the state courts finally finished with the case, the judge lifted the stay and ordered the state to re- spond to the petition. Indiana did so. Ben-Yisrayl failed to file his reply within the allotted time, so the case proceeded to decision without a reply brief from him.

The judge denied relief on all grounds without an evi- dentiary hearing. She also denied Ben-Yisrayl’s motion to alter or amend the judgment under Rule 59(e) of the Federal Rules of Civil Procedure. This appeal followed.

II. Analysis

Although Ben-Yisrayl originally sought habeas relief on six grounds, he later abandoned four of his claims and litigated only two on the merits before the district court. He argued that (1) the prosecution team intentionally destroyed exculpatory evidence; and (2) his counsel at resentencing was constitutionally ineffective for submitting a meager two- page sentencing memorandum and for failing to challenge the prosecution’s destruction of evidence. Notably, Ben-Yisrayl never mentioned the sole claim he now advances on appeal, which is an attack on his counsel’s alleged failure to introduce a “mountain” of mitigation evidence at resen- tencing. Indeed, a reference to mitigation evidence first pops up in Ben-Yisrayl’s Rule 59(e) motion, and even then it appears only in passing in a sentence about the district court’s denial of an evidentiary hearing: “Without an eviden- tiary hearing, [Ben-Yisrayl] cannot show what mitigation evidence his trial lawyers failed to present or why they failed to present it.”

Ben-Yisrayl’s omission of this claim from his habeas peti- tion is a waiver. It is well settled that waiver rules apply in the habeas context: “Claims not made in the district court in a habeas petition are deemed waived and cannot be raised for the first time on appeal.” Johnson v. Hulett , 574 F.3d 428, 432 (7th Cir. 2009). The fleeting reference to this claim in Ben-Yisrayl’s Rule 59(e) motion cannot save it for appellate review; it is equally well settled that a Rule 59(e) motion is not an appropriate vehicle for advancing “arguments or theories that could and should have been made before the district court rendered a judgment.” County of McHenry v. Ins. Co. of the W. , 438 F.3d 813, 819 (7th Cir. 2006) (quoting LB Credit Corp. v. Resolution Tr. Corp. , 49 F.3d 1263, 1267 (7th Cir. 1995)).

Indiana also invokes procedural default, but we have no need to address that argument. Waiver resolves this entire appeal. Because Ben-Yisrayl’s habeas petition never raised a claim based on his counsel’s failure to introduce mitigation evidence at resentencing, the claim is waived. The judgment of the district court is A FFIRMED

[1] At that time Ben-Yisrayl was known as Greagree Davis.