FLAUM, Circuit Judge.

Petitioner, Alton Coleman, was convicted of first-degree murder and aggravated kidnapping by an Illinois jury and sentenced to death. The United States District Court for the Northern District of Illinois denied his petition for writ of habe-as corpus. For the reasons set forth below, we affirm the decision of the district court.

I. Background

An Illinois state court jury found Alton Coleman guilty of the murder and aggravated kidnapping of nine-year-old Vernita Wheat. Her decomposed body, with her feet and hands bound, had been discovered in an abandoned building. The cause of death was deemed to be ligature strangulation. 1 Coleman represented himself at trial. At the time Coleman was convicted of the Wheat murder, he had already been convicted and sentenced to death on the basis of three subsequent murders, two in Ohio and one in Indiana.

Following Coleman’s Illinois conviction for the murder of Vernita Wheat, the court commenced a capital sentencing hearing. At the first stage of the hearing, the jury found that Coleman was eligible for the death penalty under two separate theories provided for by Illinois statute: (1) Coleman had been “convicted of murdering two or more individuals,” Ill.Rev.Stat.1983, ch. 38, para. 9-1(b)(3); and (2) the victim was under the age of twelve when she was killed and “the death resulted from exceptionally brutal and heinous behavior indicative of wanton cruelty,” Ill.Rev.Stat.1983, ch. 38, para. 9-1(b)(7). At the second stage of the capital sentencing hearing, the prosecution introduced evidence detailing Coleman’s crimes, including his prior convictions for other murders.

The Illinois jury sentenced Coleman to death, as well as to a term of fifteen years’ incarceration on the kidnapping conviction. On direct appeal, the Illinois Supreme Court affirmed Coleman’s convictions and sentences. Coleman then filed a petition pursuant to the Illinois Post-Conviction Hearing Act. Ill.Rev.Stat.1983, ch. 38, para. 122-1 et seq. The trial court denied Coleman’s post-conviction claims, and the Illinois Supreme Court affirmed the trial court’s denial.

Having exhausted his state court appeals, Coleman petitioned the United States District Court for the Northern District of Illinois for a writ of habeas corpus pursuant to 28 U.S.C. § 2254. The district court denied Coleman’s petition on all grounds. Coleman now appeals from the final judgment of the district court denying his petition for writ of habeas corpus.

II. Analysis

Coleman attacks the validity of the Illinois death sentence. Under the 1996 Anti-terrorism and Effective Death Penalty Act amendments to Section 2254 (“AEDPA”), our role in this case is limited. In order to procure habeas relief on his legal claims under AEDPA’s standard, Coleman is required to show that an Illinois state court adjudication made on the merits of a federal constitutional question “was contrary to, or involved an unreasonable application of, clearly established Federal law, as deter *796 mined by the Supreme Court of the United States,” 28 U.S.C. § 2254(d)(1), or “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding,” 28 U.S.C. § 2254(d)(2).

Coleman’s first challenge to his conviction is based on the claim that the first capital-eligibility factor under which he was sentenced to death is unconstitutionally vague. That capital-eligibility factor provides for a possible death sentence when “the murdered individual was under 12 years of age and the death resulted from exceptionally brutal or heinous behavior indicative of wanton cruelty.” Ill.Rev.Stat.1983, ch. 38, para. 9-l(b)(7). Coleman argues that this provision does not provide objective criteria for identifying the class of crimes for which the death penalty is appropriate, and fails to adequately constrain the discretion of jurors in imposing the death penalty. See Lewis v. Jeffers, 497 U.S. 764, 774, 110 S.Ct. 3092, 111 L.Ed.2d 606 (1990) (quoting Godfrey v. Georgia, 446 U.S. 420, 428, 100 S.Ct. 1759, 64 L.Ed.2d 398 (1980) (plurality opinion) (noting that capital-eligibility factors serve to “channel the sentencer’s discretion by clear and objective standards that provide specific and detailed guidance”)).

Petitioner bolsters his argument by citation to Supreme Court precedent holding unconstitutional language similar to that contained in the Illinois statute. In one case, the Court held the language “outrageously or wantonly vile, horrible or inhuman” to be unconstitutionally vague. Godfrey, 446 U.S. at 432, 100 S.Ct. 1759. In a similar holding, the Court found the phrase “especially heinous, atrocious, or cruel” to offend the constitutional requirement that capital-eligibility factors be sufficiently precise. Maynard v. Cartwright, 486 U.S. 356, 363-64, 108 S.Ct. 1853, 100 L.Ed.2d 372 (1988). Coleman contends that in light of these holdings, the terms “exceptionally brutal or heinous” and “indicative of wanton cruelty” are too subjective for the challenged provision to be upheld.

We acknowledge that the language used in this capital-eligibility factor raises a legitimate constitutional question. Nevertheless, like the district court, we decline to reach this issue and instead accept ar-guendo that the factor in question is unconstitutional. A final decision as to the constitutionality of this capital-eligibility factor should be left for a time when such a determination is necessary. Where, as here, the defendant’s eligibility for the death penalty is based on two independent factors, a finding that one factor satisfies constitutional mandates can be sufficient under appropriate circumstances for us to uphold the imposition of the death penalty. See Stringer v. Black, 503 U.S. 222, 232, 112 S.Ct. 1130, 117 L.Ed.2d 367 (1992). Before considering whether such circumstances exist here, we must first determine whether the Illinois courts’ application of the second challenged capital-eligibility factor is constitutional.

Coleman argues that the application of the second of the two capital-eligibility factors used in- sentencing him to death contravenes the constitutional requirement of “fair notice.” The eligibility factor in dispute here provides:

A defendant who at the time of the commission of the offense has attained the age of 18 or more and who has been found guilty of murder may be sentenced to death if ...

... the defendant has been convicted of murdering two or more individuals under subsection (a) of this Section or under any law of the United States or of any state which is substantially similar to subsection (a) of this Section regardless of whether the deaths occurred as the result of the same act or of several *797 related acts so long as the deaths were the result of either an intent to kill more than one person or of separate premeditated acts....

Ill.Rev.Stat.1983, ch. 38, para. 9-1(b)(3). This factor was not applied to Coleman on the basis of a murder committed prior to the Vernita Wheat murder. Rather, it was applied on the basis of subsequent out-of-state murders for which Coleman was convicted prior to the Illinois trial.

Coleman argues that this application of the challenged eligibility factor did not provide constitutionally-required “fair notice.” “[T]he notice requirements of the Due Process Clause” require that a criminal law “clearly define the conduct prohibited” as well as “the punishment authorized.” United States v. Batchelder, 442 U.S. 114, 123, 99 S.Ct. 2198, 60 L.Ed.2d 755 (1979). A statute is constitutionally defective if it “do[es] not state with sufficient clarity the consequences of violating a given criminal statute.” Id. In other words, a criminal statute must be “ ‘sufficiently explicit to inform those who are subject to it what conduct on their part will render them liable to its penalties.’” Bouie v. City of Columbia, 378 U.S. 347, 351, 84 S.Ct. 1697, 12 L.Ed.2d 894 (1964) (quoting Connally v. General Constr. Co., 269 U.S. 385, 391, 46 S.Ct. 126, 70 L.Ed. 322 (1926)).

Our inquiry is confined to whether the Illinois Supreme Court’s decision on the notice issue involved an unreasonable application of clearly established Federal law as determined by the United States Supreme Court. 28 U.S.C. § 2254(d)(1). The Illinois Supreme Court has interpreted section (b)(3), consistent with its plain meaning, to refer to prior “convictions,” not prior offenses. People v. Albanese, 104 Ill.2d 504, 85 Ill.Dec. 441, 473 N.E.2d 1246, 1259 (1984). Although Albanese was decided after the offense for which the Illinois jury sentenced Coleman to death, the Illinois Supreme Court held in People v. Coleman, 168 Ill.2d 509, 214 Ill.Dec. 212, 660 N.E.2d 919, 939-40 (1995) (Coleman II), that the statute was sufficiently explicit to have placed Coleman “on notice that after the murder of Vernita Wheat, the commission of additional murders in Illinois or another jurisdiction would make him eligible for the death penalty.”

Coleman attacks this decision by the Illinois Supreme Court as unreasonable because it allows his death sentence to turn on after-the-fact decisions by out-of-state prosecutors in Indiana and Ohio to seek murder convictions against him. But such contingencies are not fatal to fair notice, nor are they unrelated to Coleman’s own conduct. At the time Coleman murdered Vernita Wheat, he was on notice that by doing so, he would be eligible for the death penalty if the sentencer found that he had previously been convicted of murder. We cannot conclude that the Illinois Supreme Court’s decision to that effect was unreasonable.

While the Court assumes for the purposes of this appeal that the first capital-eligibility factor under which Coleman was found eligible for a death sentence is unconstitutionally vague, we conclude that the Illinois courts’ application of the second capital-eligibility factor is constitutional. Having done so, we must now proceed to consider whether the jury’s consideration of a presumed unconstitutional capital-eligibility factor so infected the sentencing process that the decision of the Illinois jury must be set aside. Our analysis depends in part on whether or not Illinois is, in capital punishment terminology, a “weighing” state.

The distinction between a “weighing” state and a “non-weighing” state is a functional one, and is best illustrated by the differences between the capital punishment sentencing schemes in Georgia and Mississippi. See Clemons v. Mississippi, 494 U.S. 738, 744-45, 110 S.Ct. 1441, 108 L.Ed.2d 725 (1990). In Georgia, which is a non-weighing state, the jury is instructed *798 not to give any particular weight to statutory aggravating factors once it has found the defendant eligible for the death penalty. See Zant v. Stephens, 462 U.S. 862, 872, 103 S.Ct. 2733, 77 L.Ed.2d 235 (1983). Rather, the jury is told to “ ‘take[ ] into consideration all circumstances before it from both the guilt-innocence and the sentence phases of trial.’ ” Id. (quoting the Georgia Supreme Court). By contrast, in a weighing state like Mississippi, once a defendant has been found eligible for the death penalty the jury is instructed to weigh only the statutory aggravating factors against the mitigating evidence in determining whether a death sentence is appropriate. See Clemons, 494 U.S. at 745, 110 S.Ct. 1441. It is this exclusive focus on statutory aggravating factors that characterizes a weighing state, as opposed to the more sweeping evidentiary consideration undertaken by juries in nonweighing states. See id.; Williams v. Cain, 125 F.3d 269, 283 (5th Cir.1997) (noting that a weighing state requires the jury “to focus only on the statutory aggravating factor[s]”) (emphasis added). Whether Illinois is a weighing or non-weighing jurisdiction can only be determined by a careful consideration of the state’s capital punishment sentencing scheme.

Illinois conducts its capital sentencing hearings in two stages: the capital-eligibility stage and the sentencing stage. In the first stage, the jury determines whether the defendant is eligible for the death penalty. In order to find that the defendant is eligible for a death sentence, the jury must unanimously determine that the defendant is over eighteen years of age, and that at least one of ten enumerated aggravating factors is present. Ill.Rev.Stat.1983, ch. 38, para. 9-1(b). If an aggravating factor is deemed to apply, the jury then proceeds to “consider aggravating and mitigating factors as instructed by the court and ... determine whether the sentence of death shall be imposed.” Ill.Rev.Stat.1983, ch. 38, para. 9-1(g). In making its determination as to the death sentence, the jury considers, but is not limited to, aggravating and mitigating factors enumerated by statute. Ill.Rev.Stat.1983, ch. 38, para. 9-1(e). “If the jury determines unanimously that there are no mitigating factors sufficient to preclude the imposition of the death sentence, the court shall sentence the defendant to death.” Ill.Rev.Stat.1983, ch. 38, para. 9-1(g).

Coleman argues that the jury’s balancing of aggravating and mitigating factors, as described above, makes Illinois a weighing state. See Morgan v. Illinois, 504 U.S. 719, 721-22, 112 S.Ct. 2222, 119 L.Ed.2d 492 (1992) (describing the “balance” of aggravating and mitigating factors that occurs at the second stage of an Illinois capital sentencing hearing). We cannot accept this analysis. The distinction between a weighing and non-weighing state in capital punishment terms is a functional one, and the mere use of the word “weighing” to describe the process of balancing aggravating and mitigating factors is not sufficient to make Illinois a weighing state. See Williams v. Calderon, 52 F.3d 1465, 1477 (9th Cir.1995) (explaining that the distinction between weighing and non-weighing states does not turn on the use of the word “weighing” to describe a state’s capital punishment sentencing scheme); see also Stringer v. Black, 503 U.S. 222, 231, 112 S.Ct. 1130, 117 L.Ed.2d 367 (1992) (“[T]he difference between a weighing State and a nonweighing State is not one of ‘semantics.’ ”). As we noted above, the key element of a capital punishment scheme in a weighing state is the exclusive use of statutory aggravating factors when balancing against mitigating considerations during the second stage of the capital sentencing hearing, as distinct from the more general balance of aggravating and mitigating factors that occurs in non-weighing states. See Cain, 125 F.3d at 283.

The definitive classification of Illinois as a weighing or non-weighing state is a question for Illinois courts. Hampton v. Page, 103 F.3d 1338, 1342 (7th Cir.1997). *799 While in the past we noted that Illinois had yet to attach “a label — in bold letters — to its capital sentencing scheme,” we also stated that the Illinois Supreme Court had not remained entirely silent on the matter. Id. Even at that time, the Illinois Supreme Court had stated that “Illinois has a non-weighing statutory scheme to determine if someone is eligible for the death penalty.” People v. Todd, 154 Ill.2d 57, 180 Ill.Dec. 676, 607 N.E.2d 1189, 1198 (1992). Recently, the Illinois Supreme Court confirmed this conclusion by unequivocally declaring that “Illinois is a non-weighing state.” People v. Shaw, 186 Ill.2d 301, 239 Ill.Dec. 311, 713 N.E.2d 1161, 1182 (1999) (citing 720 ILCS § 5/91 (c) (West 1996)). We are not free to ignore the Illinois Supreme Court’s interpretation of Illinois law, and we therefore proceed to analyze Coleman’s claim in light of our understanding that Illinois is a non-weighing state. See Stringer, 503 U.S. at 235, 112 S.Ct. 1130.

The determination that Illinois is a non-weighing state has significant implications for our review of this case. As opposed to the situation in a weighing state, where invalid statutory aggravating factors serve to allow additional evidence to erroneously come before the jury, the jury in this case properly considered the way in which Vernita Wheat was killed. Even if the manner in which Vernita Wheat was killed should not have come before the jury as a statutory aggravating factor, the circumstances surrounding her death could have been introduced by the prosecution as additional aggravating evidence. In such a circumstance there is no constitutional violation “[a]ssuming a determination by the state appellate court that the invalid factor would not have made a difference as to the jury’s determination.” Stringer v. Black, 503 U.S. 222, 232, 112 S.Ct. 1130, 117 L.Ed.2d 367 (1992). The Illinois Supreme Court made precisely that determination when it found that the jury’s reliance on the first capital-eligibility factor, “even if [it] was improper, did not affect its finding that the defendant was eligible for the death penalty.” People v. Coleman, 544 N.E.2d 330, 342 (1989). In light of this conclusion by the Illinois Supreme Court, we find no constitutional violation in the jury’s consideration of an assumed invalid statutory aggravating factor, nor do we find any error in the district court’s adjudication of the issue.

Lastly, Coleman argues that the district court erred in denying habeas relief on the claim that he was not competent to waive counsel. After waiving his right to counsel, Coleman represented himself at the capital murder trial and at the second stage of the capital sentencing hearing; he was represented by counsel only at the first stage of the sentencing hearing. The state post-conviction court conducted an evidentiary hearing on the issue and ruled that Coleman was competent to waive counsel. The Illinois Supreme Court affirmed the decision of the post-conviction court. Coleman II, 168 Ill.2d 509, 214 Ill.Dec. 212, 660 N.E.2d 919, 929 (Ill.1995). In its denial of Coleman’s habeas petition, the district court held that the Illinois courts’ treatment of this issue was not “unreasonable” for the purposes of 28 U.S.C. § 2254(d)(2).

AEDPA requires that a petitioner receive a Certificate of Appealability for each claim he seeks to appeal. 28 U.S.C. § 2253(c). Coleman does not dispute that he neither sought nor obtained a certificate for his competency claim. Rather, he argues that we should now grant the certificate under 28 U.S.C. § 2253(c)(2), which allows us to grant such a certificate and reach the merits of his claim only if he can make a “substantial showing of the denial of a constitutional right” warranting review.

Coleman has not made the requisite “substantial showing” in this case. We are satisfied with the district court’s holding that the Illinois Supreme Court correctly determined that a criminal defendant may *800 only waive counsel if he is able to rationally understand the nature and purpose of the proceedings against him and assist in his defense, and that competence to waive counsel is measured by the same standard as competence to stand trial. Godinez v. Moran, 509 U.S. 389, 113 S.Ct. 2680, 125 L.Ed.2d 321 (1993). We are also satisfied with the district court’s finding that the state court’s rejection of Coleman’s competency claim, under Godinez, was not unreasonable in light of the evidence. 28 U.S.C. § 2254(d)(2). For these reasons, we decline to grant Coleman the Certificate of Appealability he now requests.

III. Conclusion

In light of the foregoing, we Affirm the district court’s denial of the petition for writ of habeas corpus.

Affirmed.

Notes

. For a detailed account of the manner and circumstances surrounding the death of Vernita Wheat, see the Illinois Supreme Court’s opinions in People v. Coleman, 129 Ill.2d 321, 135 Ill.Dec. 834, 544 N.E.2d 330 (1989) and People v. Coleman, 168 Ill.2d 509, 214 Ill.Dec. 212, 660 N.E.2d 919 (1995).