ORDER

In 1990, an Illinois jury found Michael Savickas guilty of first degree murder. He now appeals the district court’s denial of his claim, contained in his petition for habeas corpus relief under 28 U.S.C. § 2254, that the jury was improperly instructed at his trial. We affirm.

On March 31, 1988, Savickas shot and killed Thomas Vinicky outside a Chicago tavern. Before the shooting, Savickas had argued with several persons inside the tavern, including owner Robert Walensky. Vinicky, who occasionally worked at the tavern, was not involved in any of the disputes that occurred inside, and left through the tavern’s side door during one of the altercations. Walensky threw Savickas out of the tavern after Savickas pulled out a gun and verbally abused Walensky. Savickas, who by now was outside the tavern, banged on the bar window with what Walensky believed to be the gun. In order to keep Savickas from re-entering the premises, Walensky grabbed a baseball bat and exited the front door of the bar. Once outside, Walensky witnessed Savickas shoot Vinicky in the chest as Vinicky was stepping backward. Walensky then ran back into the tavern, told the patrons inside that Vinicky had been shot and needed an ambulance, and retrieved a pistol from behind the bar. He then returned outside to Vinicky’s body, accompanied by Daniel Chaplics and other patrons. Vinicky did not have a weapon in his hands or lying near him. Savickas, meanwhile, ran away to a nearby parking lot, where the Chicago police found and arrested him. Vinicky died at a hospital later that same evening. Consequently, Savickas was charged with first degree murder.

Walensky was the state’s primary witness at Savickas’s trial. During his testimony, Walensky admitted his two prior felony convictions and also confessed that several days after the shooting he met with attorney Robert Cooley and offered to change his testimony to Savickas’s benefit if Savickas’s father paid him $200,000. Cooley, however, was an informant for the federal government and prepared memoranda regarding the meeting, which were produced during Savickas’s trial. Additionally, Walensky conceded at trial that he had never told the grand jury or the police that he returned to the bar after the shooting to retrieve his pistol.

Savickas, who also testified at trial, admitted shooting Vinicky but claimed self-defense. He explained that he did bang on the window after he was kicked out of the tavern, but did not do so with his gun. Additionally, he testified that he started to walk away from the bar when he heard a voice say, “you’re a jagoff,” at which point he turned around to see Vinicky. He testified that Vinicky yelled “I’m going to waste you,” reached in to his jacket, and began to pull out a gun. According to Savickas, upon seeing Vinicky with a gun, he pulled out his own gun and shot Vinicky.

The jury found Savickas guilty of first degree murder. He was sentenced to 28 years in prison. The Court of Appeals of Illinois affirmed his conviction, and the Illinois Supreme Court denied Savickas leave to appeal. Savickas’s state post-conviction petition was also unsuccessful. On April 23, 1997, Savickas filed his federal petition for collateral relief, which the district court denied. The district court subsequently granted Savickas’s request for a certificate of appealability solely on the issue of whether the trial court should have instructed the jury regarding the shifting burden of proof when a defendant *527raises the issue of self-defense. Savickas now appeals.1

Savickas argues in this appeal that the trial court improperly instructed the jury. During his direct appeal of this issue, the Illinois appellate court agreed with Savickas that, under Illinois law, the state had the burden of negating self-defense beyond a reasonable doubt once Savickas raised that affirmative defense. People v. Savickas, 280 Ill.App.3d 322, 171 Ill.Dec. 713, 594 N.E.2d 1233, 1240 (1992). Nevertheless, the appellate court concluded that the trial judge’s failure to incorporate this burden into the jury charge was harmless. Id. at 341, 171 Ill.Dec. 713, 594 N.E.2d 1233. The appellate court reasoned that the jury had never been told that it was Savickas’s burden to prove self-defense and, in fact, the state conceded during closing argument that it had the burden of disproving self-defense. Moreover, the court explained, there was a “dearth of evidence” in the record supporting Saviekas’s claim of self-defense. Id. Lastly, the appellate court reasoned that the jury’s verdict could not have been different with an additional self-defense instruction. Id.

We cannot conclude that the Illinois appellate court’s adjudication of Savickas’s jury instruction claim “resulted in a decision that was contrary to, or involved an unreasonable application of’ the facts or clearly established federal law. 28 U.S.C. § 2254(d). Savickas’s argument here that the state had the burden of disproving his affirmative defense does not address the real question, which is whether the trial court’s failure to instruct on self-defense harmed the outcome of the case. See Neder v. United States, 527 U.S. 1, 12, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (the issue “is not whether a jury instruction that omits an element of the offense was error ... but whether the error is subject to harmless-error analysis”). Although Savickas believes that, pursuant to Sullivan v. Louisiana, 508 U.S. 275, 113 S.Ct. 2078, 124 L.Ed.2d 182 (1993), the trial court’s omission of a self-defense instruction could not have been harmless, Sullivan involved a defective “reasonable doubt” instruction, a fundamental error that cannot be harmless. See id. at 280, 113 S.Ct. 2078; compare Neder, 527 U.S. at 15, 119 S.Ct. 1827 (limiting Sullivan to cases involving “a defective ‘reasonable doubt’ instruction”). Savickas does not contest that the trial court correctly recited the standard of reasonable doubt and thus he has not demonstrated that the Illinois court was unreasonable in applying harmless error review to his jury instruction claim. See Lanier v. United States, 220 F.3d 833, 837-40 (7th Cir. 2000) (in appeal of denial of motion under 28 U.S.C. § 2255, applying harmless error standard to analysis of jury instruction omitting an element of the offense); Gilbert v. Moore, 134 F.3d 642, 647 (4th Cir. 1998) (with regard to an appeal of the denial of a § 2254 petition, analyzing unconstitutional burden-shifting instruction under harmless error standard); Koonce v. Pepe, 99 F.3d 469, 471-476 (1st Cir. 1996) (harmless error analysis used in appeal of denial of § 2254 petition to examine whether a jury instruction misstating that the defendant held the burden of proof for an element of offense of murder necessitated habeas relief); Everette v. Roth, 37 F.3d 257, 261-262 (7th *528Cir. 1994) (applying harmless error analysis to appeal of denial of § 2254 petition claiming that trial court failed to instruct jury on self-defense at close of murder trial).

Nor can we say that the state appellate court misapplied the harmless error standard to the case at hand. First, the Illinois appeals court utilized the correct test to assess the harmfulness of the omission of a self-defense jury-instruction: whether, beyond a reasonable doubt, “the error complained of did not contribute to the verdict obtained.” Neder, 527 U.S. at 15, 119 S.Ct. 1827 (citations and internal quotations omitted). In applying this standard, the appeals court pointed out that during closing argument the state explained its burden in disproving self-defense. Furthermore, the court explained that there was a “dearth” of evidence supporting Savickas’s claim of self-defense. Finally, the court concluded that the evidence supporting Savickas’s murder conviction was such “that the jury’s verdict could not have been different had additional instructions been given.” Saviekas here has not established that these conclusions were contrary to or an unreasonable application of federal law. See § 2254(d). And, although he points to several facts that he claims corroborate his testimony regarding self-defense, none of these facts either supports or belies his claims to self-defense. Thus, the district court properly denied Savickas’s request for collateral relief.

For the foregoing reasons, we AFFIRM the decision of the district court. We also DENY Savickas’s motion to expand the scope of his certificate of appealability.