Petitioner Richard R. Desrosier appeals from the district court’s denial of his petition for a writ of habeas corpus, claiming that he did not knowingly or intelligently plead guilty to second-degree murder in Massachusetts Superior Court because he had not been adequately informed of the elements of the offense. We affirm.
Desrosier was indicted on one count each of first- and second-degree murder for killing a young woman in Worcester in April 1990. As related by the Commonwealth at the plea hearing, the evidence against him included the testimony of an acquaintance that a foursome consisting of himself, Desrosier, the victim, and another, underage, girl had obtained vodka and beer on the day of the killing and had gone up to the roof of a defunct railroad terminal to drink it. At some point, Desrosier and the victim were left alone. When the acquaintance returned, over Desrosier’s protest, he saw that the victim’s prone and unclad body was engulfed in flames. Des-rosier then stated that he had killed the victim because she had refused to have sex with him.
The acquaintance fled the scene but later returned with the police, who found the victim’s body on a lower section of the roof of the terminal, nineteen feet below an opening on the level where Desrosier had last been seen. The Commonwealth also recounted the statements of a number of other people who had interacted with Des-rosier in the wake of the murder. Their proffered testimony was that Desrosier had blood on his clothing and hands which he acknowledged was another person’s blood, and that Desrosier told them that he had just killed someone. The police also retrieved clothing from Desrosier’s *40home with stains matching the victim’s blood type.
At the plea hearing, Desrosier conceded that he had no reason to doubt that the killing had occurred in the manner described but explained that he had no independent recollection of the events of that evening because he had “blacked out” from drinking. Desrosier, who described himself at the time as a twenty-three year-old high-school graduate, also testified that he understood the difference between the sentences for first- and second-degree murder with respect to parole.1 He further stated that his lawyer had discussed with him the Commonwealth’s evidence, “the defenses [he] could raise and the other things [he] could do if [he] had a trial,” and “the pros and cons of having a trial, as opposed to entering a plea of guilty.” His counsel, with whom Desrosier said he was satisfied, added that Desrosier had been given copies of the police reports prepared as part of the murder investigation as well as a transcript of the probable cause hearing, which he had “reviewed ... many times.” The Superior Court accepted Des-rosier’s plea to second-degree murder and sentenced him to a mandatory term of life in prison.
Some five years later, Desrosier moved to withdraw his plea, arguing, inter alia, that he had not been sufficiently informed of the elements of first- or second-degree murder.2 A different Superior Court justice from the one who had taken the plea held an evidentiary hearing, at which Des-rosier was represented by different counsel. At this hearing, Desrosier called as a witness his former defense attorney, who testified that, prior to the entry of the plea, the two of them had “assessed everything, and we discussed it,” including the police and autopsy reports, the probable cause hearing, the main witnesses, and defense counsel’s investigation. Desrosier did not testify.
The Superior Court granted the motion, ruling that “because there is no record that the defendant was ever specifically informed of the elements of murder in the first or second degree, including the requisite level of intent needed to commit such crimes, the defendant’s plea was not freely and understanding^ made.” Massachusetts v. Desrosier, No. 90-2097, slip op. at 10 (Mass.Super.Ct. Nov. 7, 2000). Specifically, the court found that the judge who took the plea “failed to discuss any of the elements of the murder charges, including intent, in his colloquy even after the defendant claimed he had a ‘blackout.’ ” Id. The court also concluded that Desrosier’s statements at the plea hearing were “not specific enough to demonstrate that [he] was fully informed of the elements of the crime.” Id.
The Commonwealth appealed this decision to the Massachusetts Appeals Court, which reversed. Massachusetts v. Desrosier, 56 Mass.App.Ct. 348, 778 N.E.2d 1 (2002). While observing that “it would have been preferable had the plea hearing judge explained the elements of murder in the first and second degrees at the plea hearing,” the Appeals Court nevertheless concluded that “the record demonstrates that the defendant did, in fact, plead freely and understandingly.” Id. at 6. The court noted that
*41the defendant heard a detailed recitation of the evidence against him, and stated that he did not have any reason to doubt the veracity of that evidence; he acknowledged he admitted [the] killing ... to numerous persons; [he] affirmed he had discussed possible defenses with his attorney; defense counsel testified, he had discussed the evidence with the defendant, and they had ‘assessed everything’; and there is no suggestion that the defendant was not on notice of the charges contained in the indictment.
Id. at 8. Citing specifically to Desrosier’s statements at the plea hearing, the Appeals Court reasoned that “as a matter of common sense, a discussion of ‘defenses’ and the ‘pros and cons of having a trial’ would not take place in isolation,” but “almost certainly would have referred to the elements of the crimes to which the defenses would be advanced.” Id. at 6-7. The court ruled that, as such, the record demonstrated that Desrosiers had been advised of the elements of the offense as required by Henderson v. Morgan, 426 U.S. 637, 96 S.Ct. 2253, 49 L.Ed.2d 108 (1976). 778 N.E.2d at 5-6.
After the Massachusetts Supreme Judicial Court denied his application for further appellate review, 438 Mass. 1104, 782 N.E.2d 515 (2003), Desrosier filed a petition for a writ of habeas corpus in federal district court, claiming that the decision of the Appeals Court amounted to an unreasonable application of Supreme Court precedent under the Antiterrorism and Effective Death Penalty Act of 1996, 28 U.S.C. § 2254(d) (2007) (“AEDPA”). The petition was referred to a magistrate judge, id. § 636(b)(1)(B) (2007), who recommended that it be denied. The magistrate judge determined that the Appeals Court had not unreasonably applied Supreme Court precedent when it held “that discussions between [Desrosier] and his lawyer necessarily included advice concerning elements of the crime with which [Desrosier] was charged,” and that “although reasonable minds could disagree as to the [Appeals Court’s] findings of fact, those findings are not unreasonable in light of the record which was available to [it]” (footnote omitted). Desrosier v. Bissonette, No. 03-40194, slip op. at 10-11, 12 (D.Mass. Dec. 19, 2005).
The district court adopted the magistrate judge’s report and recommendation over Desrosier’s objections. The court reasoned that, because the elements of second-degree murder “are neither complex nor esoteric ... it is hardly unbridled conjecture to draw the inference that, in the course of assessing and discussing ‘everything’ about the case, [Desrosier] was made aware by counsel that the Commonwealth had to prove he intended to cause the victim’s death.” Desrosier v. Bissonette, No. 03-40194, slip op. at 6, 7 (D.Mass. Sept. 19, 2006). (footnote omitted). Desrosier then applied for, and was granted, a certificate of appealability on the issues of whether the Appeals Court’s decision involved an unreasonable application of Supreme Court precedent or an unreasonable determination of the facts. This appeal followed.
In considering an appeal from a denial of a petition for habeas corpus, we review the district court’s legal conclusions de novo. See, e.g., Furr v. Brady, 440 F.3d 34, 36-37 (1st Cir.2006). Under AEDPA, a federal court cannot grant ha-beas relief “with respect to any claim that was adjudicated on the merits in State court proceedings” unless the state court decision (1) “was contrary to, or involved an unreasonable application of clearly established Federal law, as determined by the Supreme Court of the United States” or (2) “was based on an unreasonable determination of the facts in light of the *42evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d). We agree with the magistrate judge and the district court that the Appeals Court’s decision suffers from neither of these infirmities.
“A guilty plea operates as a waiver of important rights, and is valid only if done voluntarily, knowingly, and intelligently.... Where a defendant pleads guilty to a crime without having been informed of the crime’s elements, this standard is not met and the plea is invalid.” Bradshaw v. Stumpf 545 U.S. 175, 183, 125 S.Ct. 2398, 162 L.Ed.2d 143 (2005) (citing Henderson, 426 U.S. at 647, 96 S.Ct. 2253). As the Appeals Court noted, this rule does not require the judge who took the plea to have explained the elements of the offense to the defendant, provided that the record adequately reflects that defense counsel did so. Id. The record need not, however, contain defense counsel’s explicit affirmation to that effect. “[EJven without such an express representation, it may be appropriate to presume that in most cases defense counsel routinely explain the nature of the offense in sufficient detail to give the accused notice of what he is being asked to admit.” Henderson, 426 U.S. at 647, 96 S.Ct. 2253.
Contrary to Desrosier’s contention, the Appeals Court did not unreasonably apply these federal constitutional rules for a valid guilty plea. While the court did not invoke, by name, a “presumption” that defense counsel had explained the elements of second-degree murder to Desrosier, its reasoning was entirely consistent with that aspect of Henderson. Based on Desrosier’s admissions at the plea hearing that he had discussed the “defenses” and the “pros and cons of having a trial” with his former attorney, as well as on the attorney’s testimony at the motion hearing that he and his client had “discussed” and “assessed everything,” the Appeals Court concluded that defense counsel had informed Desro-sier of the elements of the charge of second-degree murder.3 Massachusetts v. Desrosier, 778 N.E.2d at 5-7. Given that the Supreme Court has never required defense counsel to say outright that he or she has discussed the elements of the crime with the defendant in order for a constitutionally valid plea to result-in-deed, Henderson in applying the presumption holds to the contrary-the Appeals Court did not unreasonably apply federal law.4
*43Though Desrosier does not argue that the Appeals Court’s decision was based on an unreasonable determination of the facts, that idea permeated both his brief and oral argument in this case. In particular, he objects to what he sees as the Appeals Court’s essentially discarding the motion court’s finding that his prior attorney did not, in fact, inform him of the elements of second-degree murder. We see things differently. The Appeals Court simply disagreed with the motion court about the legal significance of the fact that defense counsel did not expressly state that he recited the elements to Desrosier. In any event, federal courts cannot grant habeas relief based on mere disagreements with how a state court conducts its appellate review. In other words, “state-court judgments must be upheld unless, after the closest examination of the state-court judgment, a federal court is firmly convinced that a federal constitutional right has been violated.” Williams v. Taylor, 529 U.S. 362, 388, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (plurality opinion). We are unconvinced that anything approaching the unconstitutional happened here.
Furthermore, to the extent that the Appeals Court did resolve any facts in overturning the Superior Court’s decision, Des-rosier has the burden to show, by clear and convincing evidence, that those factual determinations were unreasonable. 28 U.S.C. § 2254(e)(1). He has not done so. Indeed, he has never come forward with any evidence to contradict his former attorney’s version of events or to negate the inference that they did in fact discuss the elements of second-degree murder. It is not enough for him simply to argue for the contrary inference at this point. The district court properly dismissed Desrosier’s petition.
Affirmed.