Petitioner Leonard Wellington (“Wellington”) brought a habeas corpus action pursuant to 28 U.S.C. § 2254 (2000), alleging that his trial counsel was ineffective for failing to obtain alibi testimony. The district court denied Wellington relief, finding that he could not demonstrate prejudice as a result of his counsel’s deficient performance. We affirm.
BACKGROUND
The State of Florida charged Wellington with the crimes of robbery with a deadly weapon and two counts of false imprisonment. After entering a not guilty plea, Wellington proceeded to trial where a jury found him guilty as charged. At trial, Detective Molly McIntyre testified that the police received the initial call regarding the robbery at the Rite Aid drug store at 9:56 p.m. When she arrived at the scene, she spoke with several individuals who gave her descriptions of the suspect whom the authorities later identified as Wellington. She also testified that later in her investigation, a detective from Fort Lauderdale, Florida, gave her reason to believe that Wellington might have been involved in the robbery.
John Locke (“Locke”), the manager of a Publix grocery store located near the Rite Aid store, testified at trial that a short time before the robbery, a black male entered the Publix asking to use the restroom. Locke described the black male as approximately 6 feet, 2 inches tall, weighing about 180 to 200 pounds, with a mous-tache and shave “bumps” on his neck. Locke stated that the male wore a black baseball cap and a satin/silky suit that was brownish/copper in color. Locke looked at a photo line-up and identified Wellington as the man he saw on the night of the robbery. He commented that the mous-tache he saw on the night in question was different from the one shown in the photo line-up. Locke later picked the defendant out of a live line-up and, when he selected Wellington, stated that he “was very sure” that Wellington was the man he saw the night of the robbery. (R. Vol.2, Exh. 5, p. 37). Looking at Wellington at trial, Locke stated that he was “positive” that he was the man he saw in the Publix that night. (Id at 45).
Cynthia Waring, a Publix employee, testified at trial that on the night of the robbery, a black male bought sunglasses from her and she placed the sunglasses in a small brown paper bag. Jean Wade, the Rite Aid manager, testified that two days after the robbery, she found a small brown paper bag in the store and Rite Aid did not utilize such bags.
Vivian Gehringer (“Gehringer”), a Rite Aid employee and victim of the robbery, testified that on the night of the robbery, she noticed a black male with a black baseball cap enter the store. At first, she thought he appeared to be wearing glasses. Later, she saw that the glasses were wrap-around reflective lens sunglasses. When he approached her, he had an automatic nine millimeter handgun which she *1259recognized because her husband, who was a retired police officer, had a nine millimeter handgun. The man with the handgun asked Gehringer to take him to the office, so she led him in that direction. Another employee, Colleen Fahey (“Fahey”) was in the office. The man told Fahey to get on the floor, turn her back to him, and not look at him. Gehringer stated that he instructed her to open the safe, which she did. Then he told her to turn around and not look at him. Out of the corner of her eye, she saw him put on gloves and put the money into a bucket. (Id. at 73). The man talked to Fahey, asking if she had children. When he finished, he told them not to do anything, wait a few minutes and then “do what you have to do.” (Id. at 74). After he left, Gehringer called the authorities.
In describing the suspect, Gehringer stated that he had on a bronze, brown colored silk type shirt with long sleeves and no collar. He had a small growth on his upper lip and he was about 5 feet 10 inches to 6 feet tall and weighed about 185 pounds. Gehringer commented that the male was well-dressed and well-spoken. Ironically, she found him to be “soft-spoken” and “calm,” with a “kind” voice. (Id. at 75). “He sounded like a very nice man.” (Id.). Gehringer was unable to identify the suspect in a photo line-up, but at the live line-up, she identified Wellington by his voice. Gehringer stated that she narrowed it down to two men and, after she asked them to speak, she knew the robber was Wellington. She stated that she was “100% sure” it was the robber’s voice. (Id. at 77).
The State rested and the defense did not call any witnesses. Defense attorney George Allen (“Allen”) presented the first and final closing arguments. After deliberating, the jury returned guilty verdicts on both counts.
Wellington appealed his case to the Florida District Court of Appeal, which affirmed without written opinion. Wellington v. State, 729 So.2d 940 (Fla.Dist.Ct.App.1999) (Table). Wellington filed a post-conviction motion pursuant to Rule 3.850, Florida Rules of Criminal Procedure (1999), arguing that his counsel was ineffective for failing to call Wellington’s parents as alibi witnesses. The state trial court conducted an evidentiary hearing on Wellington’s motion for post-conviction relief. The trial court denied his motion and, on appeal, the state appellate court affirmed. Wellington then filed a timely petition for habeas corpus relief in federal district court. A magistrate judge issued a report and recommendation, recommending that the district court deny Wellington’s petition for relief. The district court adopted the magistrate judge’s recommendation and denied Wellington a Certificate of Appealability (“COA”). This court granted a COA on the sole issue of whether Wellington’s counsel was ineffective for failing to obtain alibi testimony.
STANDARD OF REVIEW
Wellington’s petition for habeas corpus is governed by the Anti-Terrorism and Effective Death Penalty Act (“AED-PA”). Pursuant to 28 U.S.C. § 2254(d), a federal court may issue a petition for habe-as corpus relief only if the state court’s ruling “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States” 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); see also Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). “Unless a state court decision is directly contrary to Supreme Court case law, we review state court findings of fact and conclusions of *1260law for reasonableness.” Van Poyck v. Fla. Dep’t of Corr., 290 F.3d 1318, 1321 (11th Cir.2002). We review de novo the district court’s determination of whether the state court’s findings and conclusions are reasonable. Id.
DISCUSSION
Since AEDPA governs this appeal, we must first determine whether the state court identified and applied the correct governing legal principles. We then consider whether the state court’s application of the governing legal principles was contrary to, or involved an unreasonable application of, clearly established federal law as determined by the United States Supreme Court.
A. Governing Legal Principles
It is well established that the Supreme Court’s decision in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), is the “controlling legal authority” to be applied to ineffective assistance of counsel claims. Williams, 529 U.S. at 406, 120 S.Ct. at 1512 (O’Connor, J., concurring). To succeed on a claim of ineffective assistance of counsel, the petitioner must show both incompetence and prejudice. Chandler v. United States, 218 F.3d 1305, 1312 (11th Cir.2000) (en banc), cert. denied, 531 U.S. 1204, 121 S.Ct. 1217, 149 L.Ed.2d 129 (2001). The petitioner’s burden of demonstrating prejudice is high. Under the prejudice prong, “[i]t is not enough for the defendant to show that the errors had some conceivable effect on the outcome of the proceeding.” Strickland, 466 U.S. at 693, 104 S.Ct. at 2067. Instead, the petitioner “must show that ‘there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.’” Chandler, 218 F.3d at 1312-13 (quoting Darden v. Wainwright, 477 U.S. 168, 184, 106 S.Ct. 2464, 2473, 91 L.Ed.2d 144 (1986)). “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Strickland, 466 U.S. at 694, 104 S.Ct. at 2068.
The state court correctly identified the Strickland standard in evaluating Wellington’s claim of ineffective assistance of counsel. Thus, it applied the controlling legal principles, as required by AEDPA, in ruling on Wellington’s claim of ineffective assistance of counsel.
B. Contrary To
“Under the ‘contrary to’ clause, a federal habeas court may grant the writ if the state court arrives at a conclusion opposite to that reached by this Court on a question of law or if the state court decides a case differently than this Court has on a set of materially indistinguishable facts.” Williams, 529 U.S. at 412-13, 120 S.Ct. at 1523 (O’Connor, J., concurring). The “contrary to” clause “suggests that the state court’s decision must be substantially different” from the controlling legal precedent. Fugate v. Head, 261 F.3d 1206, 1216 (11th Cir.2001), cert. denied, - U.S. -, 122 S.Ct. 2310, 152 L.Ed.2d 1065 (2002) (quoting Williams, 529 U.S. at 405, 120 S.Ct. at 1519). A state court’s decision that applies the correct legal rule would not fit within the “contrary to” clause even if the federal court might have reached a different result relying on the same law. See Williams, 529 U.S. at 404-06, 120 S.Ct. at 1519-20 (O’Connor, J., concurring).
In this case, the state court, by correctly identifying Strickland as the controlling legal authority on claims of ineffective assistance of counsel, did not reach an opposite conclusion from the Supreme Court on a question of law. Further, Wellington does not cite to any decision in which the United States Supreme Court, faced with materially indistinguishable *1261facts, reached a decision different from the state court in this case. Therefore, the state court’s decision was not “contrary to” clearly established federal law as determined by the United States Supreme Court.
C. Unreasonable Application
We next consider whether the state court’s decision involved an “unreasonable application” of clearly established federal law as determined by the United States Supreme Court. “Under the ‘unreasonable application’ clause, a federal habeas court may grant the writ if the state court identifies the correct governing legal principle from this Court’s decisions but unreasonably applies that principle to the facts of the prisoner’s case.” Williams, 529 U.S. at 414, 120 S.Ct. at 1523 (O’Connor, J., concurring). In deciding this issue, the federal court should consider whether the state court’s application of the law was objectively unreasonable and should not apply the subjective “all reasonable jurists” standard. Id. at 409-10, 120 S.Ct. at 1521-22. The Supreme Court recently adhered to its pronouncements in Williams, stating that “we stressed in Williams that an unreasonable application is different from an incorrect one.” Bell v. Cone, 535 U.S. 685, 122 S.Ct. 1843, 1850, 152 L.Ed.2d 914 (2002). The Court further noted that “a federal habeas court may not issue a writ under the unreasonable application clause ‘simply because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly.’ ” Id. (quoting Williams, 529 U.S. at 411, 120 S.Ct. at 1522 (O’Connor, J., concurring)).
Under the stringent Williams standard, we hold in the present case that the state court’s determination that Wellington could not show that he suffered prejudice from his counsel’s deficient performance1 was reasonable. See Brown, 272 F.3d at 1313 (“It is the objective reasonableness, not the correctness per se, of the state court decision that we are to decide.”). We now consider the “unreasonable application” prong.
At trial, Locke and Gehringer gave descriptions of a suspect that were similar— the suspect was wearing a black baseball cap and a satiny, brownish/copper suit. Locke said he had a moustache, and Geh-ringer said he had a small growth on a moustache. Locke said he was about 180 to 200 pounds, and Gehringer said he was about 185 pounds. Locke positively identified Wellington from a live line-up as the man who entered the Publix store shortly before the robbery at the Rite Aid. Geh-ringer positively identified Wellington at a live line-up by his voice.
At the Rule 3.850 hearing, Wellington’s attorney, Allen, testified that he was aware of an alibi defense; he failed to file a notice of alibi; he failed to timely notify the State of Wellington’s mother, Mary Ann Allen’s (“Mrs. Allen”), availability to testify; and he failed to investigate Wellington’s father, Herman Allen (“Dr. Allen”), as a witness. He concluded that his decision not to call alibi witnesses “was not a tactical decision.” (R. Vol. 2, Exh. 14, p. 20); cf. Tarver v. Hopper, 169 F.3d 710, 716 (11th Cir.1999) (stating that a lawyer’s “admissions of deficient performance” were not persuasive). Contradictorily, Allen also stated that although it was error not to call the alibi witness, he “thought *1262[he] was making the best decision for [his] client at that time.” (R. Vol.2, Exh. 14, p. 16).
Mrs. Allen stated that she and her husband met with attorney Allen to discuss their availability as alibi witnesses. Mrs. Allen informed the attorney that Wellington was home with her and her husband on the night in question. She stated that they had “an agreement” that he would be home when he was supposed to be there. (Id. at p. 40). She had a meeting with the attorney to discuss her “son’s present incarceration.” (Id. at 43). Mrs. Allen testified that the attorney told her that family members were not always the best witnesses.
Dr. Allen testified that he also told the attorney he was home with Wellington on the night in question. He stated that he “checked on [Wellington] to make sure that he was at home because [sic] probation officer was checking by and we just made sure that he stayed there.” (Id. at 60). Dr. Allen could -not clearly distinguish the night in question from any other night. Wellington, testifying at the hearing, stated that he told his attorney that he was home on the night of the robbery and his parents could confirm that fact. He also testified that he and his attorney discussed his decision not to testify. (Id. at 67).
Nikki Robinson Morgan (“Morgan”), the assistant state attorney who prosecuted Wellington, testified that when she reviewed the case file, Mrs. Allen’s name was on the witness list. When Allen told her that Wellington’s mother was going to testify as to alibi, Morgan told him that she would object because he did not file a notice of alibi. On the day of trial, Allen told Morgan that he was not going to call Wellington’s mother and commented that he wanted to save his first and last argument.2 Morgan thought that Allen’s decision not to put on an alibi witness and to save his first and last argument was smart. (Id. at 92). Morgan also commented that Dr. Allen’s testimony would not have provided Wellington any help because he had nothing to offer. In all, Morgan thought Allen did a good job by impeaching the State’s witnesses as far as the identification. She stated that, “I thought he was quite effective. And I thought he made smart strategic turns, decisions all the way through the trial.” (Id. at 93).
As the trial court found, there is no reasonable probability that the alibi testimony would have changed the outcome of Wellington’s trial. The State presented the testimony of one witness who positively identified Wellington as being in the vicinity shortly before the robbery and the testimony of a victim witness who was “100% sure” that Wellington was the man who robbed her. The victim witness identified Wellington by his voice, and the trial court found that Wellington did have a distinctive voice, just as Gehringer described. See 28 U.S.C. § 2254(e)(1) (factual determinations by a state court shall be presumed to be correct); see also Robinson v. Moore, 300 F.3d 1320 (11th Cir.2002). Moreover, as Gehringer testified, Wellington instructed her to lead him to the office, and after she opened the safe, Wellington told her not to look at him. Because she was unable to see him during most of the robbery, Gehringer was not able to concentrate on Wellington’s physical appearance as much as his voice.
Furthermore, as the prosecuting attorney noted, Dr. Allen’s alibi testimony would not have been helpful. He was unable to distinguish the night of the robbery from any other night. Additionally, *1263the fact that Mrs. Allen would have testified that her son was home on the night of the robbery would have been subject to cross-examination as to why she remembered that particular night so clearly. The prosecutor would have elicited the fact that Wellington’s parents were keeping close watch over him because he was on probation.3 As such, there is no reasonable probability that the alibi testimony would have changed the outcome of Wellington’s trial. Accordingly, the trial court’s application of Strickland’s prejudice prong was not objectively unreasonable.
CONCLUSION
The state trial court correctly identified the Strickland standards as the governing legal principles to apply to Wellington’s claim of ineffective assistance of counsel. The trial court’s application of Strickland to Wellington’s claim was neither “contrary to” nor an “unreasonable application” of clearly established federal law as determined by the United States Supreme Court. Accordingly, we affirm the district court’s judgment denying Wellington habe-as relief.
AFFIRMED.
. We need not discuss the performance deficiency component of Wellington’s ineffective assistance claim because failure to satisfy the prejudice component is dispositive. Brown v. Head, 272 F.3d 1308, 1313 (11th Cir.2001), peí. for cert. filed, August 16, 2002 (No. 02-5967).
. This discussion between counsel was not a part of the trial record and Allen testified that he did not remember commenting to the prosecutor about the first and last argument.
. Whether Mrs. Allen’s testimony that her son was on probation would have lent credence to her testimony is clearly debatable. In fact, had Wellington’s counsel called Wellington’s mother as a witness, it is likely that she would have disclosed Wellington’s prior conviction during her cross-examination. The damage to his defense would have outweighed any questionable value her alibi testimony would have provided. As the State’s attorney noted at oral argument, the fact that he was debating that fact with the court bolsters the conclusion that the trial court's finding was not unreasonable.