OPINION

SUTTON, Circuit Judge.

Dwight Rashad, a Michigan prisoner serving a life sentence for possessing more than 650 grams of cocaine, filed a petition for a writ of habeas corpus. See 28 U.S.C. § 2254. The district court denied the petition. We affirm.

I.

At 9:30 p.m. on September 7, 1988, Dwight Rashad pulled up to his girlfriend's house in suburban Detroit and proceeded inside carrying a black briefcase. As luck would have it, the police were conducting surveillance of the house and had a warrant to search it for evidence of drug trafficking. Officers executed the warrant thirty minutes later. A drug-sniffing dog reacted positively to a locked closet in the basement, and when officers pried off the lock they found several kilograms of cocaine inside. Continuing their search of the house, officers opened Rashad's black briefcase and found a key inside that opened the cocaine-filled closet in the basement. Officers arrested Rashad and impounded his car. A few weeks later, based on a separate warrant, they searched the car, where they found several kilograms of cocaine hidden behind a quarter panel.

The State charged Rashad with possession of more than 650 grams of cocaine with intent to deliver it. In April 1989, a jury convicted him of the lesser-included offense—possession of more than 650 grams of cocaine. At the time, this offense required a mandatory sentence of life in prison without the possibility of parole. See Harmelin v. Michigan, 501 U.S. 957, 961 n. 1, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991). Yet the trial court held that the sentence violated the state constitution's ban on cruel and unusual punishment and sentenced Rashad to 40 to 100 years in prison instead.

Rashad appealed the conviction, and the State cross-appealed the trial court's ruling that the mandatory life sentence was unconstitutional. In June 1992, the Michigan Court of Appeals affirmed Rashad's conviction but reversed his sentence, holding that a mandatory life sentence did not violate the state constitution. The Michigan Supreme Court denied leave to appeal in May 1993.

Rashad waited more than a decade for the trial court to resentence him. Prompted by a motion for resentencing filed by Rashad in March 2004, the court held a new sentencing hearing in May 2004. Two significant changes in Michigan's sentencing laws had taken place over the prior twelve years. First, in June 1992, the Michigan Supreme Court held that the without-parole component of this kind of life sentence violated the state constitution's ban on cruel and unusual punishment and mandated that parole be made available to defendants convicted under the statute. People v. Bullock, 440 Mich. 15, 485 N.W.2d 866, 877-78 (1992). Second, in March 2003, the Michigan legislature amended the State's drug laws to eliminate the mandatory-life component of such sentences. Under the new statute, a defendant convicted of possessing 450 to 1000 grams of a controlled substance is not subject to a mandatory minimum and is subject to a statutory maximum of 30 years in prison. Mich. Comp. Laws § 333.7403(2)(a)(ii). Applying the (constitutional) statutory penalties in effect when Rashad committed his crime, the trial court resentenced him to life in prison with the possibility of parole.

Rashad appealed his new sentence, arguing that the trial court should have sentenced him under the no-mandatory-minimum version of Michigan's drug laws. Reviewing this argument for plain error because Rashad had not raised it in the trial court, the Michigan Court of Appeals affirmed Rashad's sentence on the ground that the new sentencing provisions do not apply retroactively to defendants who committed their crimes and were convicted before the amendments went into effect. The Michigan Supreme Court denied leave to appeal.

In December 2008, Rashad filed a federal habeas petition raising six errors: two concerning the jury instructions given at his original trial; two challenging his sentence of life in prison with the possibility of parole; one challenging the admission of evidence seized during the search of the house; and one alleging ineffective assistance of appellate counsel. The district court denied Rashad's petition, and we granted a certificate of appealability.

II.

At the outset, the State urges us not to reach the merits of three of Rashad's claims—two jury instructions, one evidentiary ruling—on the ground that AEDPA's statute of limitations bars consideration of them. AEDPA requires a state prisoner to file a habeas petition within one year of "the date on which the judgment became final by the conclusion of direct review or the expiration of the time for seeking such review." 28 U.S.C. § 2244(d)(1)(A). Rashad's judgment, as the State sees it, became final in 1993 after the state appellate courts affirmed his conviction, giving him until April 24, 1997—one year after AEDPA's effective date—to file his petition. See Searcy v. Carter, 246 F.3d 515, 517 (6th Cir.2001). If the State is correct, Rashad missed the deadline by more than a decade. One premise of the State's argument is straightforward: A judgment in a criminal case typically becomes final after direct review by the state courts and the United States Supreme Court or at the end of the time for seeking such review. See Jimenez v. Quarterman, 555 U.S. 113, 119-20, 129 S.Ct. 681, 172 L.Ed.2d 475 (2009).

Another premise is not. Although the Michigan appellate courts affirmed Rashad's conviction in 1993, they threw out his sentence and remanded the case for resentencing. When does a petitioner's "judgment bec[o]me final," § 2244(d)(1)(A), in this setting? After direct review of the conviction? Or after direct review of the new sentence imposed at resentencing?

Burton v. Stewart, 549 U.S. 147, 127 S.Ct. 793, 166 L.Ed.2d 628 (2007) (per curiam), it seems to us, shows that the judgment becomes final after direct review of the new sentence. A jury convicted Burton of rape, robbery and burglary in 1994. The state appellate courts affirmed his conviction but vacated his sentence, and the trial court resentenced him in March 1998. Burton filed an unsuccessful habeas petition in December 1998 challenging his conviction, and he filed another petition in 2002 challenging the constitutionality of his new sentence. Id. at 149-52, 127 S.Ct. 793. The Court held that Burton's 2002 petition was "second or successive" because it, like his previous petition, challenged his 1998 judgment. Id. at 153, 127 S.Ct. 793. Rejecting Burton's submission that he had to file the first petition challenging his conviction in 1998 or the claims would have been time-barred, the Court said that for purposes of AEDPA's statute of limitations, "[f]inal judgment in a criminal case means sentence. The sentence is the judgment." Id. at 156, 127 S.Ct. 793. The clock thus "did not begin until both his conviction and sentence became final by the conclusion of direct review ... [,] which occurred well after Burton filed his 1998 petition." Id. at 156-57, 127 S.Ct. 793.

Burton's situation parallels Rashad's in all material ways. Burton's 1998 petition raised claims challenging his conviction from several years before, but the statute of limitations had not yet started to run because direct review of the new sentence he received on resentencing was not yet complete. So too here. Rashad filed his petition within the limitations period after direct review of his new sentence ended. Rashad timely filed all of his claims, including those challenging the underlying conviction.

A contrary approach would require Rashad to bifurcate the claims arising from his criminal case into distinct judgments—one related to the conviction, one related to the sentence. Yet the AEDPA statute of limitations speaks of one "judgment," § 2244(d)(1)(A), not many. And Burton tells us the "judgment in a criminal case means sentence." 549 U.S. at 156, 127 S.Ct. 793. Besides splitting each criminal judgment into two, the State's approach would require petitioners to comply with different limitations clocks for each judgment and, it is worth adding, would require the State to defend two cases rather than one. That approach would not advance "AEDPA's goal of streamlining federal habeas proceedings," Rhines v. Weber, 544 U.S. 269, 277, 125 S.Ct. 1528, 161 L.Ed.2d 440 (2005), as it would force prisoners who have their convictions affirmed but their sentences vacated—a "not uncommon situation," Burton, 549 U.S. at 154, 127 S.Ct. 793—to file dual petitions. A fair reading of the language of AEDPA together with Burton does not support this approach, and neither do the decisions of any other circuits. To our knowledge, all of the circuits to address this question after Burton agree that the limitations clock in this setting begins after the new sentence. See Scott v. Hubert, 635 F.3d 659, 666 (5th Cir.2011); Villaneda v. Tilton, 432 Fed.Appx. 695, 695 (9th Cir.2011) (government conceded judgment did not become final until after resentencing); Ferreira v. Sec'y, Dep't of Corr., 494 F.3d 1286, 1292-93 (11th Cir.2007); cf. United States v. Carbajal-Moreno, 332 Fed.Appx. 472, 474-76 (10th Cir.2009) (reaching same result based on similar language in 28 U.S.C. § 2255(f)(1)).

Contrary to the State's argument, Bachman v. Bagley, 487 F.3d 979 (6th Cir. 2007), does not point in a different direction. The Ohio appellate courts affirmed Bachman's rape conviction and life sentence in 1997. Id. at 980. Bachman filed a habeas petition challenging his conviction more than a year after his conviction and sentence became final, but he argued that the petition was not time-barred because the trial court's designation of him as a "sexual predator" under a new state law in April 2004 reset the statute of limitations. Id. at 980-81. We rejected the argument, holding that Bachman's "designation as a sexual predator started the running of a ne[w] statute of limitations period with respect to challenges to [that] designation only—not with respect to challenges to his underlying conviction." Id. at 983. Bachman differs from today's case because the state appellate courts affirmed Bachman's conviction and his sentence on the first round of direct review. His judgment thus became final upon the conclusion of that first round of direct review, Burton, 549 U.S. at 156-57, 127 S.Ct. 793, and he could not use his subsequent designation as a sexual predator to reopen his final conviction. Here, by contrast, Rashad's judgment did not become final after his first round of direct review because he no longer was subject to a sentence. The judgment became final upon the conclusion of direct review of the new sentence he received at resentencing. See id. at 156-57, 127 S.Ct. 793. Rashad timely filed all of his claims.

III.

Jury Instructions. At the conclusion of Rashad's 1989 trial, the court instructed the jury (1) that it could convict Rashad of the lesser-included offense of possession if it did not find him guilty of possession with intent to deliver, and (2) that it could convict him if it found that he aided and abetted the drug offense. Rashad seeks habeas relief on both instructions, contending that the State charged him only with possession with intent to deliver and the State introduced no evidence at trial that he was an aider and abetter. The Michigan Court of Appeals upheld both instructions under state law because the evidence introduced at trial supported liability as an aider and abettor, see People v. Mann, 395 Mich. 472, 236 N.W.2d 509, 511 (1975), and liability under the offense of possession, see People v. Mendoza, 468 Mich. 527, 664 N.W.2d 685, 688 (2003) (instruction on lesser-included offense appropriate if supported by the evidence); see also People v. Leighty, 161 Mich.App. 565, 411 N.W.2d 778, 784 (1987) (instruction on cognate offense appropriate if supported by the evidence).

Generally speaking, a state court's interpretation of the propriety of a jury instruction under state law does not entitle a habeas claimant to relief. 28 U.S.C. § 2254(a); Estelle v. McGuire, 502 U.S. 62, 67-68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991). The exception is when the instruction is so flawed as a matter of state law as to "infect[] the entire trial" in such a way that the conviction violates federal due process. Henderson v. Kibbe, 431 U.S. 145, 154, 97 S.Ct. 1730, 52 L.Ed.2d 203 (1977). Rashad has not met this burden. Rashad did not lack notice that he could be convicted of possession of cocaine, even though the State charged him only with possession with intent to deliver. As the names of the offenses suggest, the former is a "necessarily included lesser offense of [the latter] because the only distinguishing characteristic is the additional element of intent to deliver." People v. Torres, 222 Mich.App. 411, 564 N.W.2d 149, 153 (1997). And a conviction on the lesser-included offense does not violate Michigan law or the United States Constitution. The aiding-and-abetting instruction likewise was fair game, especially given the reality that one of Rashad's defenses was that someone else placed the cocaine in the basement closet. The government was entitled to respond to this defense by contending that it failed even on its own terms through an aiding-and-abetting theory of liability.

Search and Seizure. Rashad argues that the state trial court erred by admitting evidence found in his briefcase— namely the key to the cocaine-filled closet in the basement—because the search violated the Fourth Amendment. Longstanding precedent precludes us from granting habeas relief based on a state court's failure to apply the exclusionary rule of the Fourth Amendment, unless the claimant shows that the State did not provide him "an opportunity for full and fair litigation of [his] Fourth Amendment claim." Stone v. Powell, 428 U.S. 465, 494, 96 S.Ct. 3037, 49 L.Ed.2d 1067 (1976). Rashad cannot rise to this challenge. The trial court rejected Rashad's Fourth Amendment claims on forfeiture grounds because his attorney did not show up at the hearing designed to consider them. And the Michigan Court of Appeals rejected the claims on the merits, holding that "the briefcase was properly within the scope of the warrant" because it could have contained drugs, and the officers' "hypertechnical violation" of a state statute requiring officers to inventory all items seized during a search did not require suppression. R. 10-17, at 2, 4. Rashad had ample opportunities to present these claims in state court, precluding habeas relief. Stone, 428 U.S. at 495, 96 S.Ct. 3037.

Sentencing Claims. Rashad raises two challenges to his life sentence. He first argues that the trial court should have resentenced him under Michigan's amended drug laws (which carry no mandatory minimum) rather than the law that was in force at the time of his offense and conviction (which carried a mandatory minimum of life in prison). The Michigan Court of Appeals has held that Michigan's amended sentencing laws do not apply retroactively, which is to say they do not apply to defendants who were convicted before the amendment. See, e.g., People v. Doxey, 263 Mich.App. 115, 687 N.W.2d 360, 365 (2004). Rashad does not cite any precedent from the United States Supreme Court requiring the retroactive application of state sentencing laws. Nor are we aware of any such authority. To the contrary, courts generally presume that "legislation, especially of the criminal sort, is not to be applied retroactively" unless the legislature clearly requires otherwise. Johnson v. United States, 529 U.S. 694, 701, 120 S.Ct. 1795, 146 L.Ed.2d 727 (2000). Federal law does not entitle Rashad to retroactive application of Michigan's amended sentencing laws.

Rashad also claims that the disparity between the sentence he received under Michigan's old sentencing regime and the sentence an offender would receive under the new regime violates equal protection and due process. But the federal Constitution does not require "that two persons convicted of the same offense receive identical sentences." Williams v. Illinois, 399 U.S. 235, 243, 90 S.Ct. 2018, 26 L.Ed.2d 586 (1970). Rashad persists that he received a harsher sentence for mere possession under the old regime than what someone convicted of possession with intent to deliver would receive under the new regime. But Michigan's new drug laws, like its old ones, do not establish that possession of a large amount of cocaine is a less serious offense than possession with intent to deliver a large amount of cocaine. Defendants whose offenses involve more than 450 grams of cocaine face the same sentencing range under either statute. Compare Mich. Comp. Laws § 333.7401(2)(a)(ii) (possession with intent to deliver), with id. § 333.7403(2)(a)(ii) (possession). That Rashad, as an earlier offender, received a higher sentence than later offenders does not violate the Federal Constitution. See Doe v. Mich. Dep't of State Police, 490 F.3d 491, 504 (6th Cir. 2007). Because this claim lacks merit, so too does Rashad's final claim that his appellate counsel performed ineffectively by failing to raise the argument in the state appellate courts. See Ludwig v. United States, 162 F.3d 456, 459 (6th Cir.1998).

IV.

For these reasons, we affirm.