CUDAHY, Circuit Judge.

Six years ago, fifteen year-old Jeremy Armstrong shot and killed Robert Drury, his father's roommate. A Wisconsin state jury found Armstrong guilty of first-degree reckless homicide and he was sentenced as an adult to a prison term not to exceed 20 years. A Wisconsin Court of Appeals affirmed the conviction, and Armstrong's petition for review to the Wisconsin Supreme Court was denied. Armstrong appeals now from the Eastern District of Wisconsin's denial of habeas relief. We affirm.

I.

At age fifteen, Jeremy Armstrong was a high school student with more than his share of challenges. His time was divided between his separated parents — his mother Cheryl, who was mentally ill, and his father Robert, who was a crack addict. His father's roommate, Robert Drury, was also a crack addict and repeatedly threatened Armstrong with both physical and sexual violence. Weapons were stashed all around his father's house, and the electricity was sometimes cut off because of unpaid bills. Despite all of these negative influences, Armstrong was an honor student with a perfect attendance record.

On June 19, 1997, Armstrong heard that Drury had come into some money, money that Armstrong felt should be given to his father for repayment of a debt. Armstrong went to his father's house, confronted Drury and demanded the cash, eventually grabbing a gun and pointing it at Drury. Drury refused to hand over the money. According to witness Christopher Torres, Drury threatened to kill Armstrong and lunged for the gun. Armstrong shot Drury dead.

Armstrong was arrested and charged with first-degree intentional homicide. Following Wis. Stat. § 938.183(2), under which adult criminal courts have exclusive jurisdiction over juveniles age fifteen or older charged with first-degree intentional homicide, the state tried Armstrong as an adult. Three Wisconsin state trial court decisions are at issue here. First, Armstrong moved to suppress inculpatory statements made while in police custody. Armstrong claimed that the interrogation session that eventually resulted in his confession involved a detective's putting his hands around Armstrong's throat, knocking Armstrong's head against a wall and telling Armstrong that he would be brutally and repeatedly raped in prison. To substantiate these claims of police misconduct, Armstrong took and passed a polygraph test and moved to admit the results in support of his suppression motion. Both that evidentiary motion and the underlying suppression motion were denied by the state court.

Second, Armstrong requested jury instructions on perfect and imperfect self-defense. The court, after an instruction conference, refused to give the self-defense instructions, finding that there was insufficient evidence to support either theory of self-defense. Oddly enough, on the second day of jury deliberations, the jury sent two questions to the trial judge: "What [does] the privilege of self-defense mean? Is [Armstrong] allowed the privilege of self-defense in the act of committing a crime?" The court then discovered that the instructions sent into the jury room had accidentally included self-defense language: "If the defendant was acting reasonably in the exercise of the privilege of self defense, his conduct did not create an unreasonable risk to another." The defense moved for a mistrial and, in the alternative, for the belated issuance of an authorized self-defense instruction. Both motions were denied. Instead, the judge ordered the jury to disregard the mistakenly included self-defense language.

Third, Armstrong brought a motion to dismiss, arguing that the state statutes that guided the determination of whether Armstrong would be sentenced as a juvenile or an adult were unconstitutional as applied to Armstrong. The trial court denied that motion as well.

Although he had been charged with first-degree intentional homicide, Wis. Stat. § 940.01, the jury convicted Armstrong on the lesser offense of first-degree reckless homicide, Wis. Stat. § 940.02. Armstrong argued prior to sentencing that he should be given a juvenile disposition under Wis. Stat. § 938.183(2)(a)(2), which permitted adult criminal courts trying a juvenile to hand over the juvenile to the juvenile justice system as long as the juvenile was not convicted of first-degree intentional homicide and met certain other criteria. The court considered the factors for determining the appropriateness of waiver of eligibility for an adult sentence, Wis. Stat. § 938.18(5), but found that Armstrong did not qualify for the waiver. Armstrong was sentenced as an adult to a prison term not to exceed twenty years. His conviction was subsequently affirmed by the Wisconsin Court of Appeals. State v. Armstrong, 234 Wis.2d 524, 611 N.W.2d 470, No. 98-1768-CR, 2000 Wisc.App. LEXIS 184 (Wis.Ct.App. Mar. 7, 2000).

Armstrong's § 2254 petition in the district court challenged the above three trial court decisions. First, he argued that the Wisconsin Court of Appeals decision affirming the trial court's exclusion of polygraph evidence was contrary to United States v. Scheffer, 523 U.S. 303, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998). Second, he argued that the decision affirming the trial court's refusal to instruct the jury on self-defense was contrary to or involved an unreasonable application of Keeble v. United States, 412 U.S. 205, 93 S.Ct. 1993, 36 L.Ed.2d 844 (1973), and Mathews v. United States, 485 U.S. 58, 108 S.Ct. 883, 99 L.Ed.2d 54 (1988). Third, he challenged the decision affirming the constitutionality of the statutes governing whether Armstrong would be sentenced as a juvenile or as an adult. Armstrong argued that these statutes, as applied to him, were contrary to or involved an unreasonable application of controlling Supreme Court due process law. The district court rejected all three arguments and denied Armstrong's petition.

II.

The Antiterrorism and Effective Death Penalty Act (AEDPA), 28 U.S.C. § 2254, provides our standard of review of state court proceedings in petitions for habeas relief. The AEDPA states, in pertinent part, that habeas relief may be granted if the state court's holding "resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States." 28 U.S.C. § 2254(d)(1).

A state court decision is "contrary to" a Supreme Court precedent "if the state court arrives at a conclusion opposite to that reached by [the Supreme Court] on a question of law" or "if the state court confronts facts that are materially indistinguishable from a relevant Supreme Court precedent and arrives at a result opposite to [that precedent]." Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). Under § 2254(d)(1)'s "contrary to" clause, we review the state court decision de novo to determine, as a question of law, what is clearly established law as determined by the Supreme Court and whether the state court decision is contrary to Supreme Court law. See Schaff v. Snyder, 190 F.3d 513, 522 (7th Cir. 1999).

An application of Supreme Court precedent is unreasonable "if the state court identifies the correct governing legal rule from [the Supreme Court] cases but unreasonably applies it to the facts of the particular state prisoner's case" or "if the state court either unreasonably extends a legal principle from [Supreme Court] precedent to a new context where it should not apply or unreasonably refuses to extend that principle to a new context where it should apply." Williams, 529 U.S. at 407, 120 S.Ct. 1495. Under the "unreasonable application of" clause of § 2254(d)(1), we defer to a reasonable state court decision. Anderson v. Cowan, 227 F.3d 893, 896-97 (7th Cir. 2000).

We review de novo the district court's decision on Armstrong's petition. 28 U.S.C. § 2254(d)(1); Washington v. Smith, 219 F.3d 620, 627 (7th Cir. 2000).

A.

Armstrong's first claim is that the Wisconsin Court of Appeals' affirmance of the trial court's exclusion of polygraph evidence was contrary to United States v. Scheffer, 523 U.S. 303, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998). In Scheffer, the Supreme Court, while ruling that even a per se ban on polygraph evidence was constitutionally permissible, stated that "[i]ndividual jurisdictions . . . may reasonably reach differing conclusions as to whether polygraph evidence should be admitted." Id. at 312, 118 S.Ct. 1261. The use of polygraph evidence in Wisconsin is controlled by State v. Dean, 103 Wis.2d 228, 307 N.W.2d 628 (1981), in which the Wisconsin Supreme Court established a per se ban on polygraph evidence in criminal cases, and by Wis. Stat. § 301.132, which arguably overruled Dean in part by specifically authorizing the use of polygraph tests of convicted sex offenders by the state department of corrections.

Armstrong argues that Scheffer's declaration that each state has the authority to determine the use of polygraph tests within the state, combined with Wisconsin's arguable partial statutory overruling of Dean, somehow required the trial court here to accept Armstrong's polygraph evidence on the alleged abusive police interrogation incidents. Scheffer provides little support for Armstrong's argument. As the district court wrote: "Even if Section 301.132 can be termed an exception to Wisconsin's per se rule, [Armstrong] has failed to establish that the United States Supreme Court has held that, once any exception is made in a state's statutory scheme, polygraph evidence must be admissible in a suppression hearing." District Ct. Order at 9 (emphasis added). In other words, Armstrong cannot explain why, even if we read Wis. Stat. § 301.132 very broadly to suggest that Wisconsin courts should reconsider the Dean exclusion of polygraph evidence in contexts other than those expressly covered by the statute, the trial court should have admitted Armstrong's polygraph evidence pursuant to a Supreme Court command. The state courts' exclusion of the polygraph evidence was not contrary to Scheffer.

B.

Armstrong next claims that the trial court erred by not giving the requested self-defense instructions. Armstrong asserts that the failure to give a perfect self-defense instruction violated Mathews v. United States, 485 U.S. 58, 63, 108 S.Ct. 883, 99 L.Ed.2d 54 (1988) ("As a general proposition a defendant is entitled to an instruction as to any recognized defense for which there exists evidence sufficient for a reasonable jury to find in his favor."). Further, Armstrong argues that the failure to give an imperfect self-defense instruction violated Keeble v. United States, 412 U.S. 205, 208, 93 S.Ct. 1993, 36 L.Ed.2d 844 (1973) ("[T]he defendant is entitled to an instruction on a lesser included offense if the evidence would permit a jury rationally to find him guilty of the lesser offense and acquit him of the greater."). According to Armstrong, self-defense was relevant here because he only fired when Drury jumped toward Armstrong and, threatening to kill him, tried to grab his gun.

The trial court refused to give these instructions because it found that there was insufficient evidence to support either defense. As a matter of Wisconsin law, since Armstrong was the initial aggressor, he had no right of self-defense. See Wis. Stat. § 939.48(2)(a); Armstrong, 611 N.W.2d 470, 2000 Wisc.App. LEXIS 184, at *13 ("Like the armed gunman in Ruff, Armstrong confronted his intended robbery victim with a gun and announced that he wanted the victim's money. At that point, the right of self-defense was not available to Armstrong as an excuse or justification for killing the victim." (citing Ruff v. State, 65 Wis.2d 713, 223 N.W.2d 446 (1974))); see also 40 Am.Jur.2d Homicide § 148 (2002) ("The general rule is that one who slays another, to be justified or excused on the ground of self-defense, must be without fault in provoking the difficulty."). Although the law does permit initial aggressors to regain their right of self-defense by withdrawing from the conflict and communicating the cessation of aggression, Wis. Stat. § 939.48(2)(b); 40 Am.Jur.2d Homicide § 152, an armed gunman does not regain the right of self-defense simply because his target attempts to defend himself. See Ruff, 223 N.W.2d at 451-53. Because the evidence simply did not support a defense of self-defense, such a jury instruction would have been inappropriate. The state courts' rejection of the jury instructions was neither contrary to, nor did it involve an unreasonable application of, clearly established federal law.

Armstrong also argues that the trial court's refusal to give a self-defense instruction after the jury asked for clarification (of the inadvertently included self-defense language) merits habeas relief. That is, Armstrong's argument goes, when the jury asked about the inadvertently included self-defense jury instruction language, the court should have identified self-defense as a proper defense, rather than telling the jury to disregard the self-defense language. We see no reason, however, why the analysis after the jury's inadvertent exposure to the self-defense language should be any different from the analysis of the court's initial refusal to give the self-defense instructions. Given the mix-up in the jury instructions, the trial court did its best to minimize confusion by telling the jury to disregard the language it should not have received in the first place. While this mix-up may have served as a plausible ground for a mistrial — a motion for mistrial was denied — it certainly did not require the trial court to give jury instructions for which there was no factual basis.

C.

Armstrong's last claim is that the state courts should have found Wis. Stat. §§ 938.183(2) and 938.18(5)(b) to be un-constitutional as applied to Armstrong. Section 938.183(2), which references the criteria listed in § 938.18(5), instructs criminal courts when a juvenile in adult criminal proceedings should be given, in place of an adult criminal sentence, a juvenile disposition. While not crystal clear, Armstrong's argument appears to have two elements: (1) the statutes create an impermissible irrebuttable presumption of an adult sentence for juvenile defendants charged with intentional homicide, and (2) the statutes are void for vagueness.

According to Armstrong, the statutes at issue demand that all juveniles initially charged with first-degree intentional homicide but convicted of a lesser offense be sentenced as adults. This is because any such juvenile would clearly fall on the wrong side of the criteria set out in § 938.18(5)(b), i.e., whether the offense was violent, aggressive, premeditated and willful. The operation of these criteria, according to Armstrong, creates an impermissible irrebuttable presumption and makes any accompanying procedure pointless for the juvenile.

We agree with the state that the statute does not create such an irrebuttable presumption. Indeed, while the burden may seem impossibly high, some juveniles could hypothetically receive a juvenile disposition based on § 938.18(5)(a), (c) and (d). For example, subsection (a) takes into account, among other factors, the personality, mental health, previous record and pattern of living of the juvenile. Had the trial judge made findings on these criteria more favorable to Armstrong, it is possible that they would have outweighed the seriousness of Armstrong's offense. The language of the statute, at least, does not forbid such a hypothetical balancing. Further, even if the application of the § 938.18(5) criteria always resulted in an adult disposition for juveniles charged with intentional homicide, it is not at all clear that the statutes would be unconstitutional. For one, Armstrong provides us with no case law suggesting that the state does not have authority to impose adult sentences on all juveniles charged with intentional homicide without a hearing to determine whether the juvenile should instead be given a juvenile disposition. Although we agree that the procedure laid out in § 938.183(2) might, in most cases, have a foreordained outcome for juveniles charged with intentional homicide, it is certainly preferable to have such a process to allow for the rare exception than to have no process at all. At least, Armstrong had an opportunity to present his case for a juvenile disposition and to appeal the unfavorable decision through the state courts.

Armstrong's second argument charges that the statutes are void for vagueness. At the outset we note that it is unclear to us how statutes that Armstrong argues create an irrebuttable presumption are at the same time vague. Armstrong's argument appears to be that, in part because the statutes create an irrebuttable presumption, the statutes "do not provide notice as to what the defendant is required to prove and how to prove it." Armstrong Br. at 24. Armstrong, citing Rogers v. Tennessee, 532 U.S. 451, 121 S.Ct. 1693, 149 L.Ed.2d 697 (2001), Marks v. United States, 430 U.S. 188, 97 S.Ct. 990, 51 L.Ed.2d 260 (1977), and Eastman v. City of Madison, 117 Wis.2d 106, 342 N.W.2d 764, 769 (1984), argues that defendants in his position lack adequate notice as to what charges they face, what they stand to lose, what evidence they can bring to the hearing and what standards will be applied in judging them.

We disagree that the statutes are so vague as to be unconstitutional. Rogers and Marks are simply too far removed from the facts and law of this case to be applicable here. While they affirm general constitutional principles of notice, especially in interpreting the Ex Post Facto Clause, they are simply not on point. Eastman, a state appellate decision, actually undermines Armstrong's argument. The Eastman court found a disputed city ordinance not unconstitutionally vague in part because a mayoral memorandum in support of the ordinance "set forth ten specific criteria for determining" the reach of the ordinance. Eastman, 342 N.W.2d at 769. Section 938.18(5) delineates clear criteria within the text of the statute. Armstrong cites no other cases to bolster his argument that the statutes are so vague as to be unconstitutional, nor does our own review suggest any persuasive argument in his favor.

Moreover, Armstrong does not cite any cases in his appellate brief to refute the analysis of the lower courts: the Wisconsin Court of Appeals and the district court both held that vagueness challenges can only be made against substantive statutes prohibiting specific conduct and not against procedural statutes. See District Ct. Order at 15 (citing Giaccio v. Pennsylvania, 382 U.S. 399, 402-03, 86 S.Ct. 518, 15 L.Ed.2d 447 (1966), to support the proposition that vagueness challenges cannot be made to procedural statutes); State v. Dums, 149 Wis.2d 314, 440 N.W.2d 814, 817 (1989). We are wary of attempting to draw such a bright line between substance and procedure and do not rely on such a distinction. Nonetheless, Armstrong must cite authority that shows that the state courts' decision was contrary to or involved an unreasonable application of federal law, and he has cited no such United States Supreme Court authority to that end.

III.

For the foregoing reasons, the judgment of the district court is AFFIRMED.