BAUER, Circuit Judge.

The petitioner-appellant, Lawrence Coleman, was convicted of murder in Illinois and sentenced to 28 years in prison. Coleman was denied relief in state court and eventually filed a federal habeas petition in district court under 28 U.S.C. § 2254. The district court also denied relief; we granted a certificate of appealability. For the following reasons, we affirm the denial of the habeas petition.

I. BACKGROUND

This case arises from a murder that took place on November 30, 1998. Early that morning, a group of men affiliated with a gang known as the Renegade Vice Lords gathered outside of Jacqueline Brenaugh's apartment on the South Side of Chicago. The men believed that Jamil Caraway, a member of a rival gang, was hiding out in her apartment, and they meant to kill him. Instead, they shot and killed Jacqueline Brenaugh, when she peered out of her apartment window to get a better look at the men outside.

Detective Philip Graziano of the Chicago Police Department was assigned to the case. After some investigation, he zeroed in on Lawrence Coleman as a suspect. At about 11:30 a.m. on December 12, Detective Graziano arrested Coleman and began an interrogation. By midnight, Graziano had elicited a confession from Coleman; specifically, Coleman admitted serving as an accomplice in Brenaugh's murder. Graziano called on Assistant State's Attorney Nancy Nazarian to assist him in recording the confession. She arrived at the police station sometime around midnight of December 13, and about four hours later, a court reporter recorded Coleman's full confession.

Coleman subsequently was indicted, pleaded not guilty, and moved to suppress his confession. Central to the motion to suppress was Coleman's claim that he had invoked his right to an attorney several times and that the police had proceeded in violation of Miranda v. Arizona. The parties offered conflicting testimony on this issue at the suppression hearing; the court denied Coleman's motion, holding that "the credibility is resolved on behalf of the State." At trial, a jury found Coleman guilty of first-degree murder under an accomplice liability theory. He was sentenced to 28 years in prison.

Coleman appealed his conviction in state court, arguing, among other things, that the trial court had improperly refused to suppress his confession. He included an affidavit from his attorney, David Wiener, stating that Wiener had called the police station during the December 12 interrogation and requested that police cease questioning his client. The Illinois appellate court concluded that the suppression question came down to a credibility determination, and that the trial court had properly exercised its discretion in crediting the State's witnesses over Coleman. State of Illinois v. Coleman, No. 1-00-4022333 Ill.App.3d 1205, 296 Ill.Dec. 813, 836 N.E.2d 228 (Ill.App.Ct. Sept. 27, 2002). The court affirmed Coleman's conviction.

Coleman has mounted several challenges to his conviction over the course of many years, so a short summary of the current procedural posture is in order.

After exhausting his state post-conviction remedies, Coleman filed a pro se habeas petition in federal court pursuant to 28 U.S.C. § 2254. The district court denied relief, see U.S. ex rel. Coleman v. Shaw, No. 06C184, 2009 WL 1904370 (N.D.Ill. July 1, 2009), and Coleman responded by filing a motion to reconsider, plus several other motions. The district court consolidated the motions as a Rule 60(b) request for relief, considered each of Coleman's arguments on the merits, and rejected each one; the court then denied him a certificate of appealability. Coleman appealed to this Court; after reviewing the record, we granted a certificate of appealability, but limited to the following issue: "whether the state courts reasonably determined that Coleman did not request counsel when he was arrested or during the 17 hours he was in custody before giving a statement and, thus, whether Coleman's statement was admissible at trial." This is now the sole issue before us on appeal.

II. DISCUSSION

A. Habeas Standards of Review

We review a district court's denial of habeas relief de novo. Northern v. Boatwright, 594 F.3d 555, 559 (7th Cir. 2010). Our review of state court decisions, however, is limited by the Antiterrorism and Effective Death Penalty Act (AEDPA). Thus, when we are dealing with a state court's determination on the merits, we may only grant habeas relief if the decision "was contrary to, or involved an unreasonable application of, clearly established Federal law," 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)(1)-(2); see also Harrington v. Richter, ___ U.S. ___, 131 S.Ct. 770, 783-84, 178 L.Ed.2d 624 (2011). The relevant decision that we review under AEDPA is always the decision of the last state court to rule on the merits of the petitioner's claims.1 McCarthy v. Pollard, 656 F.3d 478, 483 (7th Cir.2011).

A state court decision is "contrary to" federal law when it "contradicts the governing law set forth in [Supreme Court] cases." Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A state court decision involves an "unreasonable application of ... clearly established federal law" when the state court "identifies the correct governing legal rule from [Supreme Court] cases but unreasonably applies it to the facts of the particular state prisoner's case."2 Id. at 407, 120 S.Ct. 1495.

Alternatively, a state court decision involves "an unreasonable determination of the facts" under § 2254(d)(2) only when the state court makes an "unreasonable error." Morgan v. Hardy, 662 F.3d 790, 798 (7th Cir.2011). We give great deference to state court factual findings. After AEDPA, we are required to presume a state court's account of the facts correct, and the petitioner has "the burden of rebutting the presumption of correctness by clear and convincing evidence." 28 U.S.C. § 2254(e)(1); Miller-El v. Dretke, 545 U.S. 231, 240, 125 S.Ct. 2317, 162 L.Ed.2d 196 (2005).

B. "Contrary to" or an "Unreasonable Application" of Federal Law Under Section 2254(d)(1)

We begin by identifying the clearly established federal law at issue here: Miranda v. Arizona and its progeny. Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966).

Once an accused is read his Miranda rights, he may invoke his right to counsel under the Fifth and Fourteenth Amendments by requesting an attorney, and the police must immediately cease the interrogation until counsel is present. Edwards v. Arizona, 451 U.S. 477, 481-82, 101 S.Ct. 1880, 68 L.Ed.2d 378 (1981). Any waiver of the Miranda right to counsel must be voluntary, knowing, and intelligent. Id. at 482, 101 S.Ct. 1880. To be voluntary, the waiver must simply be non-coerced; to be knowing and intelligent, waiver must be made with "a full awareness of both the nature of the right being abandoned and the consequences of the decision to abandon it." Moran v. Burbine, 475 U.S. 412, 421, 106 S.Ct. 1135, 89 L.Ed.2d 410 (1986). Finally, a court may only conclude that a suspect waived his Miranda rights if the "`totality of the circumstances surrounding the interrogation' reveal both an uncoerced choice and the requisite level of comprehension." Id. (quoting Fare v. Michael C., 442 U.S. 707, 724-25, 99 S.Ct. 2560, 61 L.Ed.2d 197 (1979)).

Coleman is never clear as to whether he is arguing that his state conviction was "contrary to" or represents an "unreasonable application" of clearly established federal law. Although there are separate standards associated with each of these prongs under § 2254(d)(1), he uses them interchangeably throughout his argument. We will discuss first whether the state court decision was "contrary to" federal law.

Coleman's primary argument under § 2254(d)(1) is that the state appellate court ran afoul of Edwards v. Arizona in its analysis. Edwards does indeed contain the relevant standard, but the Illinois appellate court correctly identified that standard in its decision. The state court was careful to explain that any waiver of the right to counsel must be "voluntary, knowing, and intelligent," and it found that Coleman's waiver met that standard. The court went on to explain that in determining whether waiver is knowing and intelligent, the court must consider the totality of the circumstances. This is also correct and in accord with Edwards and Moran v. Burbine. Because the state appellate court identified the correct legal standards, we now turn to whether it applied those standards reasonably under the "unreasonable application" clause. See Etherly v. Davis, 619 F.3d 654, 661 (7th Cir. 2010) (analyzing the "contrary to" and "unreasonable application" clauses in a similar fashion).

We first highlight an important distinction between Edwards and this case; in Edwards, the defendant was arrested and requested counsel during his initial interrogation. The police ceased questioning, but then failed to provide him with counsel and resumed questioning the next day. Eventually the defendant relented during interrogation and confessed to a crime. The Supreme Court held that the defendant had not "knowingly and intelligently" waived his right to counsel when interrogation resumed on the second day.

Coleman admits but downplays the crucial difference here: In Edwards, there was no question (as there is here) about whether the defendant had initially invoked his right to counsel. Instead, the question in Edwards was whether the defendant subsequently waived the right after invoking it. This is a key element in the Supreme Court's decision. It makes sense, of course; after unequivocally invoking his right to counsel, the defendant's sudden confession during interrogation without counsel on the very next day raises a suspicion that any "waiver" made was not altogether knowing and intelligent. And the decision stresses this important distinction throughout: the lower courts had misunderstood the proper standard for finding "a valid waiver of the right to counsel, once invoked." Edwards, 451 U.S. at 484, 101 S.Ct. 1880 (emphasis added). It is inconsistent with Miranda, Edwards held, for authorities to resume interrogation once a defendant in custody "has clearly asserted his right to counsel." Id. at 485, 101 S.Ct. 1880. And the Court reaffirmed the rule of North Carolina v. Butler, 441 U.S. 369, 99 S.Ct. 1755, 60 L.Ed.2d 286 (1979) that "after initially being advised of his Miranda rights, the accused may himself validly waive his rights and respond to interrogation." Id. at 484, 101 S.Ct. 1880. Only when the accused requests counsel are any "additional safeguards" necessary. Id.

In this case, Coleman was properly read his Miranda rights, and no state court found that he ever invoked his right to counsel. Because it was never invoked, there was also nothing in federal law (in Edwards or otherwise) preventing Coleman from implicitly waiving his right to counsel simply by responding to police questioning and eventually confessing.

Coleman counters that under Edwards, courts are required to examine the waiver of the right to counsel by considering the totality of the circumstances, and he insists that the Illinois appellate court failed to do so. This argument is difficult to grasp. In its review of the trial court's denial of the motion to suppress Coleman's confession, the appellate court stated that "[i]n determining whether this waiver is knowing and intelligent, a court considers the totality of the circumstances, including the characteristics of the defendant and the details of the interrogation." And indeed, the court considered a variety of factors in reviewing the waiver question, including but not limited to: (1) Coleman's claims that he did request counsel; (2) Coleman's claim that he spoke to his attorney prior to his arrest and the phone record corroborating this; (3) Detective Graziano's and Assistant State's Attorney Nazarian's claims that Coleman never requested counsel at any point during interrogation; and (4) evidence that Coleman's attorney contacted the police station during Coleman's time in custody.

Still, according to Coleman, the state court's "choice of words" proves that it was not reviewing waiver under the totality of the circumstances — words like "dispositive" and phrases like "that fact alone." Coleman cites no authority, and we are aware of none, that requires a court to use magic words in order to properly constitute an analysis under the totality of the circumstances. We simply look to the substance of the analysis to see if the court was weighing all (the "totality") of the relevant facts (the "circumstances") in reaching its decision. The state court's refusal to find certain issues "dispositive," such as evidence that Coleman phoned his attorney before his arrest, only demonstrates that the court considered that factor but refused to assign it great weight.

In Etherly v. Davis, a case involving review of the totality of the circumstances surrounding a juvenile's waiver of the right to counsel, we acknowledged that "how much weight to assign each factor... may differ from court to court, and reasonable jurists may certainly disagree." Etherly v. Davis, 619 F.3d 654, 662 (7th Cir.2010) (citing Hall v. Washington, 106 F.3d 742, 748-49 (7th Cir. 1997)). Coleman believes Etherly supports his argument, but in fact it cuts against him; we reversed a district court's grant of habeas relief in that case because the court had exceeded its authority under AEDPA to re-weigh factors properly weighed by the state court in upholding a conviction. The state court's decision, we held, was not an unreasonable application of federal law and so could not be upset by the district court on habeas review.

Even assuming that the state court in this case could have written a clearer opinion, an inarticulate decision is not enough for Coleman to obtain habeas relief. For relief to follow under § 2254(d)(1), the state court must have applied federal law unreasonably, and that is a far cry from what happened here. We will not require a particular choice of words when a court is evaluating the totality of the circumstances surrounding the waiver of the right to counsel. In this case, the state court announced the correct legal standard and proceeded to weigh all the relevant factors in a reasonable fashion. Federal law required nothing more.

Because the state court applied the correct federal law and did so reasonably, Coleman's claim under 28 U.S.C. § 2254(d)(1) fails.

C. "Unreasonable Determination of the Facts" Under Section 2254(d)(2)

Coleman argues that the state court made "an unreasonable determination of the facts" under § 2254(d)(2) in denying his Miranda claim. Specifically, he argues that it was unreasonable for the state trial court to credit the State's witnesses over his own. He further argues that, especially in light of new affidavits he presented in his state petition for post-conviction relief, he now has ample evidence to rebut the state court's factual determinations.

First, we reiterate that after AEDPA, state court factual findings are presumed correct on habeas review and may only be rebutted by "clear and convincing evidence." 28 U.S.C. § 2254(e)(1); see also Miller-El v. Dretke, 545 U.S. 231, 240, 125 S.Ct. 2317, 162 L.Ed.2d 196 (2005) (noting that "[t]he standard is demanding but not insatiable"). Coleman faces an even greater uphill battle in a case like this, where the credibility of witnesses is at the heart of the challenge. Credibility determinations made in the trial court are notoriously difficult to overturn under § 2254(d)(2). See Rice v. Collins, 546 U.S. 333, 341-42, 126 S.Ct. 969, 163 L.Ed.2d 824 (2006) ("Reasonable minds reviewing the record might disagree about the prosecutor's credibility, but on habeas review that does not suffice to supersede the trial court's credibility determination."); Morgan v. Hardy, 662 F.3d 790, 799 (showing deference to state trial court's credibility determinations under § 2254(d)(2)).

The state appellate court acknowledged evidence that Coleman called (but did not reach) his attorney around 7:00 a.m. on December 12 when he realized the police were searching for him; this would have occurred hours prior to his arrest and so could not implicate his right to counsel. The state court also noted that Coleman's attorney called the police station during his interrogation. The law is clear, and Coleman does not dispute, that an attorney cannot invoke his client's right to counsel under Miranda. See Moran v. Burbine, 475 U.S. 412, 424-28, 106 S.Ct. 1135, 89 L.Ed.2d 410 (1986). At best, this all amounts to evidence that Coleman wished to reach his attorney. The trial court simply found Graziano's and Nazarian's testimony more credible than Coleman's, and believed that it outweighed any countervailing evidence. The appellate court agreed, and we have no clear and convincing evidence before us to suggest that this determination of facts is unreasonable.

Coleman challenges one of the state trial court's factual determinations in particular. He argues that the court erroneously lent a corroborative effect to Nazarian's testimony in order to credit Graziano's story. The court relied on this corroboration, Coleman argues, when it denied his motion to suppress. Our own reading of the state trial court's transcript does not reveal any problem with Nazarian's testimony or its corroborative effect.

Graziano was present with Coleman for a much longer period of time than Nazarian. But both Graziano and Nazarian were present with Coleman from roughly 12:00 a.m. on December 13 to 4:00 a.m. that same morning when Coleman's confession was recorded. During that four-hour period, Coleman claimed at trial, he was still asking for an attorney (for example, he claimed he asked for counsel just before the court reporter showed up at 4:00 a.m.). So when Nazarian testified at the suppression hearing that Coleman never asked for an attorney, she was presumably referring to the four-hour time period during which she and Graziano were both present. There is nothing in the transcript to indicate that the court believed Nazarian meant to corroborate Graziano's account of events from earlier in the night before she arrived on the scene.

Finally, Coleman relies on affidavits produced for the first time in his state petitions for post-conviction relief to argue the state court clearly erred in its credibility determination. These affidavits were prepared years after the crime occurred by his uncle and his former girlfriend, who both claim they overheard Coleman asking to speak to an attorney when the police initially approached him. The argument about the affidavits was only presented to the state courts and to the federal district court in the context of Coleman's ineffective assistance of counsel argument. Specifically, he used the affidavits to argue that his counsel at the suppression hearing was ineffective for not calling his uncle and his ex-girlfriend to testify. Coleman now relies on the affidavits to bolster his Miranda argument under § 2254(d)(2) for the first time on appeal. It is well-established that arguments raised for the first time on appeal are waived. See, e.g., Pole v. Randolph 570 F.3d 922, 937 (7th Cir. 2009); Domka v. Portage Cnty., Wis., 523 F.3d 776, 783 (7th Cir.2008); Kunz v. DeFelice, 538 F.3d 667, 681 (7th Cir.2008). Even if a party mentioned evidence relating to the argument below, if the argument itself was not adequately developed, it is still waived. See Pond v. Michelin North America, Inc., 183 F.3d 592, 597 (7th Cir. 1999). We thus find Coleman has waived the argument regarding the affidavits as they relate to his Miranda claim.

III. CONCLUSION

For the aforementioned reasons, we AFFIRM the district court's denial of habeas relief.