Petitioners-appellants Steven D. Beem and Donald H. Henson, Jr. sought habeas corpus relief in federal district court, 28 U.S.C. § 2254, arguing that the Kansas state courts violated their federal constitutional rights by sentencing them for aggravated incest — a crime for which they had never been charged, tried, or convicted. The district court denied the petitions for habeas corpus and the petitioners’ requests for certificates of appealability. Both petitioners appealed, and their cases were consolidated for our review. A divided panel of this court decided in petitioners’ favor, vacating their convictions and sentences. We now consider the cases as an en banc court. We exercise jurisdiction pursuant to 28 U.S.C. §§ 1291 and 2253, GRANT petitioners’ requests for certificates of appealability, and AFFIRM the district court’s denial of the habeas petitions.
I. Background
Beem was charged in the District Court of Reno County, Kansas, with one count of indecent liberties with a child, Kan. Stat. Ann. § 21-3503. In 1989, a jury found him guilty, and the court sentenced him to 15 to 60 years imprisonment.1 Beem appealed his conviction, and the Kansas Court of Appeals affirmed in 1991. Beem later filed a state habeas corpus petition, Kan. Stat. Ann. § 60-1507, arguing that because he was related to his victim, he should have been charged with aggravated *1178incest rather than indecent liberties with a child pursuant to a state law rule announced in State v. Williams, 250 Kan. 730, 829 P.2d 892 (1992).2 In 1995, the trial court vacated Beem’s sentence for indecent liberties with a child and ordered resentencing, in accordance with the Kansas Supreme Court’s decision in Carmichael v. State, 255 Kan. 10, 872 P.2d 240 (1994).3 At resentencing, the court imposed a sentence of 9 to 30 years, which conforms to the sentencing range for aggravated incest. Beem appealed the new sentence, arguing that the court had violated his rights to due process and to a jury trial. The Kansas Court of Appeals affirmed, and the Kansas Supreme Court denied review.
Henson was charged in the District Court of Miami County, Kansas, with three counts of rape, Kan. Stat. Ann. § 21-3502. In 1992, a jury found him guilty on all three counts, and the court sentenced him to three consecutive sentences of 7 to 20 years each. Henson appealed, and the Kansas Court of Appeals held that, because the victim was his step-daughter, he should have been charged with aggravated incest — rather than rape — under Williams. Following Carmichael, the court vacated his sentence and remanded for resentencing in accordance with the penalty range for aggravated incest. The district court reduced the original sentences to 3 to 7 years each.
Beem and Henson filed petitions for writs of habeas corpus with the United States District Court for the District of Kansas. Petitioners challenged the constitutionality of the Carmichael remedy, arguing that it amounts to imprisonment for aggravated incest — an offense for which neither was ever charged, tried, or convicted — in violation of the Sixth Amendment’s jury-trial guarantee and the Fourteenth Amendment’s Due Process Clause. The district court denied the habeas petitions and the petitioners’ requests for certificates of appealability.4 On appeal, a divided panel of this court held that the Carmichael remedy violated petitioners’ constitutional rights, vacated their convictions and sentences, and noted that double jeopardy did not bar new trials on the charge of aggravated incest. We granted the State’s request for en banc rehearing.
II. Discussion
A. Certificates of Appealability
Petitioners ask us to grant certificates of appealability to appeal the district court’s denial of their habeas petitions. This court will only grant a certificate of appealability to a petitioner who makes “a substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253(c)(2). Because the district court “has rejected the constitutional claims on the merits, ... petitioner^] must demonstrate that reasonable jurists would find the district *1179court’s assessment of the constitutional claims debatable or wrong.” Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000).
A divided panel of this court originally granted petitioners habeas relief, and we subsequently granted the State’s request for en banc review. These developments satisfy us that reasonable jurists would find the district court’s assessment of the petitions’ constitutional claims “debatable,” and we therefore grant petitioners certificates of appealability. See id. We have jurisdiction over this appeal pursuant to 28 U.S.C. § 2253(a).
B. Standard of Review
In evaluating the district court’s denial of a habeas corpus petition, we review legal conclusions de novo and factual findings for clear error. See Davis v. Executive Dir. of Dep’t of Corrs., 100 F.3d 750, 756 (10th Cir.1996). To obtain habeas relief, petitioners must establish that the state court decisions were “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or ... [were] 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)(1)-(2).
C. Analysis of the Constitutional Claim
1. The Williams Rule and the Carmichael Remedy
The appeals before us stem from the Kansas courts’ application of a state law rule announced in State v. Williams, 250 Kan. 730, 829 P.2d 892 (1992), and Carmichael v. State, 255 Kan. 10, 872 P.2d 240 (1994). In Williams, the Kansas Supreme Court considered the interplay between two offenses: “Indecent liberties with a child” under Kan. Stat. Ann. § 21-3503 and “Aggravated incest” under Kan. Stat. Ann. § 21-3603. Id. at 894. In Williams, the State had charged the defendant with taking indecent liberties with his 14-year-old step-granddaughter. Id. at 893. Before trial, the defendant moved to dismiss the criminal complaint. Id. at 894. He argued that when a defendant is related to the alleged victim, as set forth in the aggravated incest statute, Kan. Stat. Ann. § 21-3603, “the State must charge a defendant with aggravated incest rather than indecent liberties with a child.” Id.
The Kansas Supreme Court agreed. Id. at 897. Although the two statutes both prohibited the alleged conduct, aggravated incest had a kinship requirement not present in indecent liberties with a child. Id. at 894, 897.5 Specifically, aggravated incest requires that the victim be “known to the offender to be related to the offender....” Kan. Stat. Ann. § 21-3603(1). Because of this additional requirement, the *1180court concluded that aggravated incest was a “specific” offense, as compared to indecent liberties with a child, a more “general” offense.6 Id. at 897. Under Kansas rules of statutory construction, “ ‘a special statute prevails over 'a general statute unless it appears that the legislature intended to make the general act controlling.’ ” Id. at 895 (citation omitted). Accordingly, the court held that “where a defendant is related to the victim ... the State may charge the defendant with aggravated incest for engaging in the acts prohibited [by the aggravated incest statute] but not with indecent liberties with a child.” Id. at 897.
In Carmichael v. State, the Kansas Supreme Court considered the appropriate remedy where the prosecution violated the Williams rule but the defendant raised the issue only after conviction and sentencing for rape. Carmichael, 255 Kan. 10, 872 P.2d 240, 242 (1994). The defendant argued that because he met the kinship element under the aggravated incest statute, Williams required that the court set aside his rape convictions. Id. at 241-42. The Kansas Court of Appeals had agreed, concluding that “ ‘the judgment against [the defendant] for the offense of rape where the court was without jurisdiction to decide the issue is void.’ ” Id. at 242.
The Kansas Supreme Court reversed. Id. at 247. The court held that the charging error did not deprive the trial court of jurisdiction and rejected the notion that Williams required it to vacate the defendant’s underlying rape convictions. Id. at 243-44, 247. In other words, the court held that the defendant did not suffer illegal convictions. Rather, the court identified the harm as “the imposition of an erroneous sentence,” basing its conclusion on the Kansas legislature’s intent to impose a less severe punishment for identical conduct perpetrated by a person related to the victim. Id. at 244 (emphasis added). Accordingly, the court relied on its statutory authority to “correct an illegal sentence at any time,” Kan. Stat. Ann. § 22-3504, and remanded the case with instructions “to vacate the sentence imposed for rape and resentence the petitioner for aggravated incest.” Id. at 247.
2. Characterization of the Carmichael Remedy
According to petitioners, the Carmichael remedy amounts to a court finding them guilty of and sentencing them for aggravated incest — an offense for which they were not charged, tried, or convicted. A divided panel of this court accepted this characterization of the Carmichael remedy. We disagree.
Under Carmichael, where (1) the prosecution violated the Williams rule, but (2) the defendant failed to raise any objection until after conviction and sentencing, “the proper remedy is to vacate the sentence imposed for rape and resentence the petitioner for aggravated incest.” Carmichael, 872 P.2d at 247. This language — “for aggravated incest” — creates some ambiguity in the Carmichael remedy. Resolution of this case requires us to consider whether the Carmichael remedy truly results in a sentence for aggravated incest — which would require jury findings on all elements of that crime — or whether instead the remedy merely results in a reduced sentence for the crime of conviction — rape or indecent liberties with a child7 — albeit one *1181that is determined by reference to the penalty range for aggravated incest.
Under petitioners’ interpretation, the Carmichael remedy involves (1) vacating the sentence for the general sex crime and (2) imposing a sentence for aggravated incest without an underlying conviction for aggravated incest. Under this construction, the court assumes the missing conviction, and petitioners argue that this assumption violates due process. Alternatively construed, Carmichael is merely a sentence-reduction remedy. Under this construction, the Carmichael remedy (1) leaves intact the conviction for the general sex crime and (2) reduces the sentence for the general sex crime by reference to the allowable penalty range for aggravated incest. A close analysis of Carmichael leads us to adopt the latter characterization.
First, in Carmichael, the Kansas Supreme Court did not disturb the defendant’s underlying convictions for rape. Id. at 241, 247 (rejecting defendant’s request that the court set aside his jury convictions for rape). The court made clear that Williams did not call into question the validity of the rape convictions. Id. Rather, the court remedied what it deemed “an erroneous sentence” under Kansas law. Id. at 244 (emphasis added). Consistent with Carmichael, petitioners conceded at oral argument that their recorded convictions are rape and indecent liberties with a child — not aggravated incest.
Second, in fashioning its remedy, the Carmichael court relied on its statutory authority to “correct an illegal sentence.” Id. at 245 (citing Kan. Stat. Ann. § 22-3504). The Kansas Supreme Court apparently understood its holding to be a correction of “a sentence which [did] not conform to the statutory provision, either in the character or the term of punishment authorized.” Id. (internal quotation marks and citation omitted).8
Third, this characterization of the Carmichael remedy is consistent with Williams’ underlying rationale. The Williams court based its conclusion on the Kansas legislature’s intent to punish less severely those sex-crime offenders who were related to their victim. 829 P.2d at 895. Carmichael adheres to this legislative intent by imposing “less serious” punishment on perpetrators who are convicted of general sex crimes but are related to their victims. Cf. id. It is irrelevant whether we agree or disagree with the propriety of the Kansas courts’ decision to decide the appropriate sentence for a general sex offense conviction by reference to the allowable penalty range for aggravated incest; the question is one of Kansas state law and Kansas statutory interpretation.
S. Constitutional Analysis
We must next consider whether the Kansas state courts committed constitutional error in determining the appropriate sentences for general sex offenses by reference to the allowable penalty for aggravated incest. We acknowledge that, in determining whether the petitioners were entitled to the Carmichael remedy, the Kansas state courts were required to determine whether petitioners met the kinship requirement set forth in the aggravated incest statute, Kan. Stat. Ann. § 21-3603. Crucial to our constitutional analysis, however, is the fact that the Carmichael remedy resulted in a reduction to petitioners’ sentences.
*1182The Due Process Clause only requires that aggravating sentencing factors be proven at trial. Apprendi v. New Jersey, 530 U.S. 466, 481-82, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000). As the Supreme Court has stated, “[o]ther than the fact of a prior conviction, any fact that increases the penalty for a crime beyond the prescribed statutory maximum must be submitted to a jury, and proved beyond a reasonable doubt.” Id. at 490, 120 S.Ct. 2348 (emphasis added); see also Harris v. United States, 536 U.S. 545, -, 122 S.Ct. 2406, 2418, 153 L.Ed.2d 524 (2002) ("[O]nce the jury finds all those facts [required for the maximum sentence], Ap-prendi says that the defendant has been convicted of the crime; the Fifth and Sixth Amendments have been observed; and the Government has been authorized to impose any sentence below the maximum."). In applying this constitutional rule, "the relevant inquiry is one not of form, but of effect-does the required finding expose the defendant to a greater punishment than that authorized by the jury's guilty verdict?" Id. at 494, 120 S.Ct. 2348 (emphasis added). With respect to petitioners' cases, the answer is plainly no. Accordingly, the Kansas state courts' application of the Carmichael remedy comported with due process.
Petitioners’ reliance on Cole v. Arkansas, 333 U.S. 196, 68 S.Ct. 514, 92 L.Ed. 644 (1948), is misplaced. In Cole, the Supreme Court held that “[t]o conform to due process of law, [criminal defendants are] entitled to have the validity of their convictions appraised on consideration of the case as it was tried and as the issues were determined in the trial court.” Id. at 202, 68 S.Ct. 514. In Cole, the petitioners had been tried and convicted of promoting, encouraging, or aiding an unlawful assemblage, and they challenged the constitutionality of the statutory section defining that offense. Id. at 199-200, 68 S.Ct. 514. The Supreme Court of Arkansas, however, refused to address the constitutionality of the statutory provision of conviction and instead affirmed the appellants’ convictions on the ground that they had violated a different section of the same statute. Id. at 200, 68 S.Ct. 514. That section defined a distinct crime of participating in an unlawful assemblage, which included an element of force or violence; no element of force or violence, however, had been presented to the jury as a necessary element for conviction. Id. at 199-201, 68 S.Ct. 514. The U.S. Supreme Court reversed, because the state court “ha[d] not affirmed these convictions on the basis of the trial petitioners were afforded.” Id. at 201, 68 S.Ct. 514.
In contrast to Cole, petitioners’ cases did not involve affirmation of a conviction based on one offense, where the underlying conviction was for a separate and distinct offense. Rather, the Kansas courts “affirmed [the petitioners’] convictions on the basis of the trial petitioners were afforded.” See id. at 201, 68 S.Ct. 514. Accordingly, petitioners’ cases are outside the ambit of Cole.
Petitioners’ reliance on our decision in Von Atkinson v. Smith, 575 F.2d 819 (10th Cir.1978),9 is equally unavailing. In Von Atkinson, the State had charged the defendant with sodomy under a Utah sodomy statute that did not require proof of force. Id. at 820. Under this statute, the offense carried the possibility of 3 to 20 years in prison. Id.
*1183Following the sodomy charge but before the defendant’s guilty plea or sentencing, Utah revised its sodomy law, creating two distinct offenses: (1) misdemeanor sodomy, which did not require force and was punishable by up to 6 months imprisonment, and (2) forcible sodomy, a felony punishable by 1 to 15 years imprisonment. Id. Utah law “require[d] that [the defendant] be given the benefit of the reduced penalties] provided by the new statute.” Id. at 821. Accordingly, Utah law prohibited application of the allowable sentence under the prior sodomy statute.
The Utah state court sought to impose the harsher sentence permitted under the new forcible sodomy statute. Id. at 820. Over the defendant’s objection, the court “conducted a ‘hearing’ to determine whether force had been employed in accomplishing the act of sodomy.” Id. After concluding that the defendant had used force, the state court sentenced the defendant under the forcible sodomy statute. Id.
We vacated the Utah court’s judgment, characterizing its action as “a trial and conviction for an uncharged crime.” Id. at 821. The defendant had pled guilty to sodomy under the old Utah statute — an offense which did not require the use of force. Id. Under applicable Utah law, non-forcible sodomy carried a possible penalty of no more than 6 months. Id. at 820. The Utah state court, however, sentenced defendant for the distinct offense of forcible sodomy — an offense carrying a possible penalty of 1 to 15 years. Id. at 821. We noted that “due process does not permit one to be tried, convicted or sen-fenced for a crime with which he has not been charged or about which he has not been properly notified.” Id. (citations omitted). Accordingly, we reversed, relying on Cole.
We also dismissed as “irrelevant” the state’s argument that the forcible sodomy statute carried a less severe penalty than did the old Utah sodomy statute under which the defendant was charged. Id. State law plainly mandated sentencing according to the new statute and prohibited the old statute’s harsher sentence. Id. at 820-21. Accordingly, for constitutional purposes we were required to consider the allowable sentences under the two newly defined offenses: up to 6 months for misdemeanor sodomy versus 1 to 15 years for forcible sodomy. So construed, this aspect of Von Atkinson case presented a straightforward application of the principle later articulated in Apprendi. As in Apprendi, the Utah state court’s hearing, in which it concluded that the defendant used force, “expose[d] the defendant to a greater punishment than that authorized by the [defendant’s guilty plea].” Apprendi, 530 U.S. at 494, 120 S.Ct. 2348.
With this guidance, we consider the course of events in the Kansas state courts. Petitioners do not contend that they suffered any constitutional deprivation when the State charged them with general sex crimes rather than aggravated incest. Nor do they provide us with any basis to conclude, as a matter of Kansas law or federal constitutional law, that violation of a state law charging rule invalidates the resulting conviction or precludes the imposition of a sentence.10 It is only *1184the Kansas state courts’ application of the Carmichael remedy that the petitioners contend violated their due process rights.
Because the Carmichael remedy only affected petitioners’ sentences, our constitutional analysis turns upon the “effect” of the state court’s action. See Apprendi, 530 U.S. at 494, 120 S.Ct. 2348. Here, the petitioners’ underlying convictions for general sex crimes remain intact and their sentences are less “than that authorized by the jury’s guilty verdict.” See id. We fail to see how this result falls short of the requirements of the Due Process Clause. When federal law mandates no remedy at all for a state law violation, but state law nonetheless provides a remedy in the form of a reduced sentence, we cannot conclude that federal law requires (or even permits) a federal court to order that state law provide a more generous remedy. Accordingly, we reject petitioners’ request that we vacate their reduced sentences based on their convictions for rape and indecent liberties with a child.
III. Conclusion
Petitioners challenge the Kansas courts’ remedy for a violation of a state law rule. The remedy reduced the sentences that petitioners otherwise would have served. We cannot conclude that because the Kansas courts in their discretion have provided some remedy for the violation of state law, the federal Constitution requires that they provide a more sweeping remedy. Under these circumstances, petitioners have failed to show that the Kansas courts’ disposition of their claims was “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United *1185States; 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)(l)-(2).
We therefore AFFIRM the district court’s denial of the petitions for habeas corpus.
. Beem was also charged and convicted of one count of aggravated assault, Kan. Stat. Ann. § 21-3410, but his conviction and sentence for this crime are not at issue in this appeal.
. Under Williams, where a defendant is related to his victim, the State must charge him with the more "specific” offense of aggravated incest rather than the more "general” offense of indecent liberties with a child. 829 P.2d at 897. The Williams rule is considered at length in section 11(C)(1), infra.
. Under Carmichael, where a defendant suffered a Williams violation but fails to raise the issue until after he has been tried and convicted, the proper remedy is to remand for resen-tencing in accordance with the allowable penalty range for aggravated incest. 872 P.2d at 247. We consider the Carmichael remedy in section 11(C)(1), infra.
.Although Henson had not exhausted his remedies in state court before filing his federal habeas petition, the district court excused the exhaustion requirement because the state courts' resolution of Beem's case made it futile for Henson to seek relief in state court.
. When Williams was decided, as well as at the time of petitioners' trials, Kansas defined aggravated incest as "marriage to or engaging in any prohibited act ... with a person who is under 18 years of age and who is known to the offender to be related to the offender....” Kan. Stat. Ann. § 21-3603(1). "Prohibited acts” under the statute included "[sjexual intercourse, sodomy or any unlawful sex act” and "any lewd fondling or touching of the person of either the child or the offender, done or submitted to with the intent to arouse or to satisfy the sexual desires of either the child or the offender or both.” Id. § 21-3603(2)(a)(b). This definition of aggravated incest thus included acts also prohibited by the statutes prohibiting indecent liberties with a child, Kan. Stat. Ann. § 21-3503, and rape, Kan. Stat. Ann. § 21-3502. The Kansas Legislature has since altered the definition of aggravated incest to exclude acts that are covered by the statutes prohibiting rape and indecent liberties with a child. See 1993 Kan. Sess. Laws, ch. 253, § 15 (amending Kan. Stat. Ann. § 21-3603).
. "A statute which relates to persons or things as a class is a general law, while a statute which relates to particular persons or things of a class is specific.'' Williams, 829 P.2d at 897 (citation omitted).
. We refer to rape and indecent liberties with a child generically as "general sex crimes” or "general sex offenses” in conducting our analysis.
. Under Kansas law, an "illegal sentence” also results if a sentence is "imposed by a court without jurisdiction" or "is ambiguous with respect to the time and manner in which it is to be served.” Carmichael, 872 P.2d at 245 (internal quotation marks and citation omitted). However, neither of these circumstances is present here.
. We recognize that habeas relief is only proper where a state court decision 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) (emphasis added). Nevertheless, we consider our decision in Von Atkinson as it informs our analysis of petitioners' constitutional claims under Apprendi and Cole.
. Indeed, Carmichael explicitly rejected the defendant’s request to set aside his convictions. 872 P.2d at 242, 247 (reversing the Kansas Court of Appeals’ grant of the defendant’s motion to set aside his convictions). Accordingly, even if we were to agree with petitioners that the Carmichael remedy violated their constitutional rights, we could not vacate their convictions. To do more than return the petitioners to the position they occupied prior to the alleged constitutional violation would require us to fashion both (1) a constitutional remedy and (2) a state law remedy. We are vested with the limited authority to address the former.
*1184Our review of state court decisions is limited to consideration of questions of federal and constitutional law. The underlying violation that led to the Carmichael remedy was one of purely state law. Ultimately, then, even assuming the Carmichael remedy were found to be unconstitutional, this court could not formulate an alternative remedy. Rather, we would vacate the reduced sentence and remand for further proceedings. What other remedy, if any, should apply in the absence of the Carmichael remedy would be a matter for the Kansas courts. Since the original convictions stand under Carmichael, it is quite possible that such a result would merely lead to reinstatement of the original sentences.
Significantly, it appears likely that defendants have waived any right under Kansas law to request that a court vacate their convictions. In Williams, the Kansas Supreme Court only addressed the situation before it: the defendant objected to the complaint "at the conclusion of the preliminary examination.” State v. Sims, 254 Kan. 1, 862 P.2d 359, 364 (1993). Generally, under Kansas law, the failure to challenge defects in the charging instrument before trial constitutes a waiver. Id. at 365 (citing Kan. Stat. Ann. § 22-3208(3), which provides: "Defenses and objections based on defects in the institution of the prosecution or in the complaint, information or indictment other than that it fails to show jurisdiction in the court or to charge a crime may be raised only by motion before trial.... Failure to present any such defense or objection as herein provided constitutes a waiver thereof, but the court for cause shown may grant relief from the waiver.”); see also Kan. Stat. Ann. § 22-3208(4) ("A plea of guilty or a consent to trial upon a complaint, information or indictment shall constitute a waiver of defenses and objections based upon the institution of the prosecution or defects in the complaint, information or indictment other than that it fails to show jurisdiction in the court or to charge a crime.”). Notwithstanding the waiver statutes, a defendant can attack the charging instrument for lack of jurisdiction or failure to charge a crime, in a motion to arrest judgment, which must be filed within ten days of the verdict. Sims, 862 P.2d at 365 (citing Kan. Stat. Ann. § 3502). However, a defendant cannot use a motion to arrest judgment if, under Williams, he was incorrectly charged with a general rather than a specific sex crime. Id. at 367. The Carmichael remedy thus gives the defendant the benefit of aggravated incest’s lesser penalty, even though the defendant failed to object to the charging instrument at the proper point in the proceedings.