BALDOCK, J., delivered the opinion of the court, in which SILER, J., joined. MOORE, J. (pp. 493-95), delivered a separate dissenting opinion.
OPINION
BALDOCK, Circuit Judge.A Michigan jury convicted Aaron Leigh Cyars (Petitioner) on two counts of first-degree premeditated murder, Mich. Comp. Laws Ann. § 750.316(1)(a), one count of assault with intent to commit murder, id. § 750.83, and one count of possessing a firearm during the commission of a felony, id. § 750.227b(1). The Michigan court of appeals affirmed. People v. Cyars, No. 176536, 1997 WL 33353409 (Mich.App. Feb.28, 1997) (unpublished). The Michigan Supreme Court and United States Supreme Court denied review.
Petitioner subsequently filed an application for habeas corpus in the district court pursuant to 28 U.S.C. § 2254.1 Petitioner *487asserted, among other things, he was denied effective assistance of counsel because his trial counsel failed to proffer a limiting instruction on the jury’s use of impeachment statements. The district court denied the petition. We granted a certifícate of appealability, see 28 U.S.C. § 2253(c), on the limited issue of whether Petitioner was denied his Sixth Amendment right to effective assistance of counsel. Applying the Antiterrorism and Effective Death Penalty Act’s highly deferential standard for reviewing state-court decisions, see Woodford v. Visciotti, 537 U.S. 19, 24, 123 S.Ct. 357, 154 L.Ed.2d 279 (2002) (per curiam), we affirm because the Michigan court of appeals reasonably applied the correct principle governing ineffective assistance of counsel claims to the facts of Petitioner’s case.
I.
Petitioner used and dealt crack cocaine during the summer of 1993. He sold crack primarily for two individuals, known on the streets as “Rob and Lucky” or “Batman and Robin.” Petitioner “rolled” (i.e., distributed drugs) out of a house on Asbury Park street (Asbury House) in west Detroit. Veronica Taylor resided in the As-bury House; however, Rob and Lucky “rented” the house from Taylor to use as a “crack house.” Petitioner earned roughly $100 a day, less the cost of any drugs used on the job, for his services.
Petitioner lost $700 and a handgun Rob and Lucky fronted him in July 1993. Rob and Lucky were not pleased. Lucky informed Petitioner he would have to work at the Asbury House for seven days to pay for the lost money and three days to pay for the handgun. Petitioner went to the Asbury House around midnight on August 29, 1993 to commence work. Petitioner met Thomas Lewis on the porch. Lewis, a known “henchman” for Rob and Lucky, supervised the activities at the Asbury House. Once inside, Lewis moved a refrigerator to block the house’s front door. The refrigerator served as a barricade to slow law enforcement officers in the event of a raid. All of the house’s windows had bars save the window in Taylor’s room. The house’s backdoor was also inaccessible.
Shortly after entering the house, Lewis put Petitioner to work selling drugs. Lewis told Taylor to “page” Rob and Lucky. Petitioner was scared of what might happen when they arrived. Rob and Lucky never showed, but Leatha Chri-ston arrived at the Asbury House sometime after 2:00 a.m. Christon had arranged to engage in sexual intercourse with Lewis in exchange for crack. Petitioner let Chri-ston into the house and then, by himself, moved the refrigerator back across the front door. Lewis gave Petitioner a bag of crack to sell while he was in the bedroom with Christon.2 After Lewis and Christon consummated their transaction, Petitioner again moved the refrigerator, by himself, to let Christon out of the house. The record is silent as to whether Petitioner moved the refrigerator back across the front door after he let Christon out of the Asbury House.
Nimrod Lumpkin arrived at the Asbury House around 3:00 a.m. The refrigerator was not blocking the front door when he arrived. He went straight to Taylor’s bed*488room where they smoked marijuana and crack. Lumpkin was not aware anyone else was in the house. Meanwhile, Petitioner was in the house’s other bedroom selling crack out of a barred window to customers. Lewis was lying on his stomach on a bed in the same room facing Petitioner. A handgun was on the bed next to Lewis.
Petitioner sold the crack for approximately $20 per “rock.” After Petitioner sold a $100 or so worth of crack, he would give the money to Lewis who in turn would supply him with more crack. Lewis, however, fell asleep after about an hour of work. Petitioner then got up, grabbed Lewis’s gun, and shot Lewis once in the back of the head. Shortly thereafter, Taylor yelled “what’s that?” Petitioner cracked the door to Taylor’s room and said Lewis was playing with a gun. Petitioner then immediately entered the room with the handgun pointed at Taylor who was moving toward her window and saying, repeatedly, “Aaron don’t do it.” Petitioner shot Taylor in the back of the head. Lumpkin, however, was able to kick the gun as Petitioner turned and fired in his direction. The kick redirected the shot into Lumpkin’s arm and leg. Petitioner fired again, but was out of bullets. Petitioner left the room and exited the house through its front door. Lumpkin never heard any appliances being moved after Petitioner left Taylor’s room.3
Petitioner never called the police or any paramedics after leaving the Asbury House. Instead, Petitioner visited two groups of friends and explained to them how he killed two individuals. He showed one friend, James Morrison, the gun and crack he took from the house. Later, Petitioner discarded the gun in a field and the crack in the sewer. The Detroit Police Department arrested Petitioner. He confessed to shooting Lewis, Taylor, and Lumpkin after waiving his Miranda rights.
Petitioner claimed self-defense at trial. The State called, among others, James Morrison, Don Bailey, and Todd Cyars to testify in its ease-in-chief. James Morrison was Petitioner’s friend. During the homicide investigation, and at the preliminary hearing, Morrison made the following statement:
[Petitioner] said, “Man, I shot Veronica [Taylor], Stormy [Thomas Lewis] and another basehead. Man, I popped Stormy in the head one time. I shot Veronica somewhere in the chest. I shot the other guy all over the place.”
At trial, Morrison first testified he was honest with the police during the homicide investigation and when he testified at the preliminary hearing. As the State’s examination of Morrison proceeded, however, his memory faded and he ultimately testified “[n]one of those [statements] c[a]me *489out of my mouth.” (Joint App. at 260). The State impeached Morrison with the signed statement he gave police and the preliminary hearing transcript.
The State also called Don Bailey, an acquaintance of Petitioner. The Detroit police interviewed Bailey during the homicide investigation. Bailey gave the police a signed statement in which Bailey said Petitioner told him that “[a]fter he shot Thomas [Lewis], he shot the other two people because they were witnesses.” (Joint App. at 118). At trial, the State asked Bailey if he made this statement. Bailey denied making the statement, and then later admitted making the statement, but attributed it to a person other than Petitioner.
The State also called Petitioner’s brother, Todd Cyars. During the homicide investigation, Todd Cyars gave a signed statement to the police. Todd Cyars informed the police Petitioner stated prior to the murders “he was thinking about sticking up [the Asbury] house and taking the dope” and, after the murders, stated: “I did it. I did what I said I was going to do[.]” (Joint App. 149, 162-63). At trial, Todd Cyars admitted making the statements to the police, but denied their truth and claimed they were the product of a coercive custodial interrogation.
After Morrison’s testimony on direct examination, Petitioner’s counsel asked for a limiting instruction regarding the State’s impeachment of Morrison. Specifically, counsel asked for an instruction providing that impeachment testimony did not constitute substantive proof of the matters asserted, but instead went to the believability of the witness. The trial judge responded that he had never given such an instruction and was not going to “give it from the hips.” (Joint App. 272). The judge instructed Petitioner’s counsel to prepare an instruction and, afterwards, he would be glad to look at the proposed instruction and give it at an appropriate time. Petitioner’s counsel never renewed his request for a limiting instruction, nor provided the judge a proposed instruction. The court consequently never instructed the jury on the proper use of impeachment statements. After the court’s final jury charge, Petitioner’s counsel stated “[t]he Defendant ... thinks the jury has been appropriately instructed.” (Joint App. at 337).
II.
“The writ of habeas corpus plays a vital role in protecting constitutional rights.” Slack v. McDaniel, 529 U.S. 473, 483, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). The Antiterrorism and Effective Death Penalty Act’s (AEDPA) highly deferential standard for evaluating state-court rulings, however, severely circumscribes a federal court’s ability to grant the writ. Lindh v. Murphy, 521 U.S. 320, 333 n. 7, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997). Congress enacted AEDPA “[i]n the interest of finalityt,]” Miller-El v. Cockrell, 537 U.S. 322, 326, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003), “to reduce delays in the execution of state and federal criminal sentences,” Woodford v. Garceau, 538 U.S. 202, 206, 123 S.Ct. 1398, 155 L.Ed.2d 363 (2003), “to prevent federal habeas ‘retrials[J and to ensure that state-court convictions are given effect to the extent possible under law.” Bell v. Cone, 535 U.S. 685, 693, 122 S.Ct. 1843, 152 L.Ed.2d 914 (2002). AEDPA is thus premised on Judge Learned Hand’s observation that, if courts are to survive as an institution, they cannot “become Pene-lopes, forever engaged in unravelling the webs they wove.” Jorgensen v. York Ice Mach. Corp., 160 F.2d 432, 435 (2d Cir.1947). To these ends, § 2254 provides in relevant part:
*490(d) An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim—
(1) resulted in a decision that 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).
Petitioner concedes, as he must, § 2254(d)(l)’s “unreasonable application” clause governs the disposition of his case.4 (Aplt’s Br. at 11). A federal habeas court “may grant relief under the ‘unreasonable application’ clause if the state court correctly identifies the governing legal principle from [the Supreme Court’s] decisions but unreasonably applies it to the facts of the particular case.” Cone, 535 U.S. at 694, 122 S.Ct. 1843. The Court has repeatedly stressed that “[i]n order for a federal court to find a state court’s application of [its] precedent ‘unreasonable,’ the state court’s decision must have been more than incorrect or erroneous.” Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 2535, 156 L.Ed.2d 471 (2003). Instead, the state court’s application of clearly established law must be “objectively unreasonable.” Id.
A federal habeas court, therefore, may not grant the writ simply because, in its independent review of the legal question, it is left with a firm conviction that the state court was erroneous. Lockyer v. Andrade, 538 U.S. 63, 75, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003). Quite the opposite, as the Court recently clarified, “the range of reasonable judgment can depend in part on the nature of the relevant rule.” Yarborough v. Alvarado, — U.S. -, 124 S.Ct. 2140, 2149, 158 L.Ed.2d 938 (2004). Specifically, “[a]pplying a general standard to a specific case can demand a substantial element of judgment. As a result, evaluating whether a rule application was unreasonable requires considering the rule’s specificity. The more general the rule, the more leeway courts have in reaching outcomes in case by case determinations.” Id. The federal habeas scheme thus vests state courts with the primary responsibility of determining whether a particular defendant’s constitutional rights were violated; and, a federal court may only intervene in that judgment when the state-court’s decision is objectively unreasonable. Visciotti, 537 U.S. at 27, 123 S.Ct. 357.
III.
Petitioner argues on appeal habeas relief is appropriate because the Michigan court unreasonably applied Supreme Court precedent to his ineffective assistance claim. Petitioner specifically argues the Michigan court erred in holding he did not suffer any prejudice as a result of his counsel’s failure to proffer a limiting instruction on the statements used to im*491peach the State’s witnesses at trial. See Cyars, 1997 WL 33353409, at *4.
A.
The Sixth Amendment provides a criminal defendant with the right to effective assistance of counsel because of the effect the right has on a defendant’s ability to receive a fair trial. Mickens v. Taylor, 535 U.S. 162, 166, 122 S.Ct. 1237, 152 L.Ed.2d 291 (2002). “The benchmark for judging any claim of ineffectiveness must be whether counsel’s conduct so undermined the proper functioning of the adversarial process that the trial cannot be relied on as having produced a just result.” Strickland v. Washington, 466 U.S. 668, 686, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Consequently, “defects in assistance that have no probable effect upon the trial’s outcome do not establish a' constitutional violation.” Mickens, 535 U.S. at 166, 122 S.Ct. 1237. Whether a constitutional violation occurred as a result of counsel’s assistance is determined under the familiar two-pronged Strickland test: “First, the defendant must show that counsel’s performance was deficient.... Second, the defendant must show that the deficient performance prejudiced the defense.” Strickland, 466 U.S. at 687, 104 S.Ct. 2052. We assume without deciding Petitioner satisfied the first prong. See id. at 697, 104 S.Ct. 2052 (explaining “[i]f it is easier to dispose of an ineffectiveness claim on the ground of lack of sufficient prejudice, ... that course should be followed.”).
The issue, then, is whether the Michigan court’s rejection of Petitioner’s ineffective assistance claim was an unreasonable application of Strickland’s prejudice prong. To demonstrate prejudice, “[t]he defendant must show that there is a reasonable probability that, but for counsel’s unprofessional errors, the result of- the proceeding would have been different. : A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Strickland, 466 U.S. at 694, 104 S.Ct. 2052. AEDPA circumscribes our review' of the Michigan court’s conclusion that Petitioner did not suffer any prejudice. Cf. Wiggins, 123 S.Ct. 2542. In fact, § 2254(d) “demands that [the] state-court décision[ ] be given the benefit of the doubt.” Visciotti, 537 U.S. at 24, 123 S.Ct. 357.
B.
The Michigan court reasonably applied Strickland’s prejudice prong to the facts of Petitioner’s case. The court explained that “[b]eeause the weight and strength of the untainted evidence presented in this case overwhelmingly supports defendant’s convictions, and because the error is relatively innocuous (indeed, it was not error for the prior inconsistent statements to be put before the jury, only that the jury could not consider those statements as substantive evidence), we conclude that defendant was not prejudiced in this regard.” Cyars, 1997 WL 33353409, at *3 (emphasis added). We agree. The State had the burden of proving Petitioner’s intentional killing of the victims was deliberate and premeditated. People v. Coddington, 188 Mich.App. 584, 470 N.W.2d 478, 487 (1991). “Premeditation and dehberation may be inferred from the facts and circumstances established on the record.” Id. Circumstantial evidence demonstrating premeditation includes, but is not limited to (1) the prior relationship of the parties, (2) defendant’s actions before the killing, (3) the circumstances, including the wound’s location, of the killing, and (4) -defendant’s conduct after the killing. Id.; see also People v. Anderson, 209 Mich.App. 527, 531 N.W.2d 780, 786 (Mich.App.1995). “Premeditation and dehberation require sufficient time to allow the defendant to take a second look.” Id.
*492The record overwhelmingly supports the jury’s first degree murder verdicts, as the Michigan court held, even without considering the statements used to impeach Morrison, Bailey, and Todd Cyars. A reasonable jury could infer Petitioner knew, from past experience, nefarious activities would be afoot during his visit to the crack house on August 29, 1993. The jury could also infer Petitioner formulated a plan to kill Lewis as he distributed drugs from the house’s backroom window. Indeed, Petitioner’s claim that he was scared of Rob and Lucky’s arrival at the Asbury House was undermined by the fact he could have left the house while Lewis was with Christen, but instead opted to stay and sell drugs. Petitioner sat patiently until Lewis fell asleep and then got up, stole his gun, and shot him in the back of the head. A jury could reasonably infer Petitioner had the opportunity to take a “second look” before he executed Lewis in his sleep.
A reasonable jury, moreover, could have easily rejected Petitioner’s theory that he was unable to leave the Asbury House after killing Lewis because a refrigerator, which he had twice moved himself that evening, was blocking the front door. In fact, the evidence demonstrated the refrigerator was not even blocking the front door after Petitioner shot Lewis. A reasonable jury thus could infer that instead of simply leaving the Asbury House after killing Lewis, Petitioner took a “second look” and elected to enter Taylor’s room. Upon entering Taylor’s room, Petitioner shot her in the back of the head as she pleaded with him not to kill her. A reasonable jury could thus infer Petitioner had the opportunity to take a “third look” before shooting Taylor. Petitioner then turned on Lumpkin who likely would have also been killed but for the fact Petitioner ran out of ammunition. Petitioner then left the house through its front door; the very door Petitioner claimed prevented him from exiting the house in the first instance.
After the murders, Petitioner did not call the police to inform them he had escaped from a near-death hostage situation. Instead, he told various friends about the killing and showed off the murder weapon and drugs he looted from the house. Petitioner thereafter discarded the murder weapon and drugs in a manner sufficient to prevent authorities from recovering the evidence. A reasonable jury could infer guilt from such evidence.
In sum, circumstantial evidence before, during, and after the murder supported the jury’s verdict that Petitioner intentionally killed Lewis and Taylor with deliberation and premeditation. Indeed, the Michigan court of appeals, a United States magistrate judge, and the district court have so found. Furthermore, we denied Petitioner a certificate of appealability on the claim he was denied due process of law because insufficient evidence of premeditation existed to support his first degree murder convictions. That certificate of ap-pealability denial means reasonable jurists could not find the district court’s assessment of the claim debatable or wrong. See 28 U.S.C. § 2253(c); Miller-El, 537 U.S. at 338, 123 S.Ct. 1029.
Petitioner nevertheless argues the Michigan court unreasonably applied Strickland’s prejudice prong for four reasons. First, Petitioner argues the Michigan court of appeals incorrectly applied Strickland. This argument is irrelevant under AED-PA. See Wiggins, 123 S.Ct. at 2535. Second, Petitioner argues the Michigan court misapprehended the scope of the evidence a limiting instruction would have affected and actually relied on the “tainted evidence” to affirm his conviction. The overwhelming circumstantial evidence of Petitioner’s guilt and the jury’s rejection of his *493claim of self-defense, however, is the death-knell of this argument. See also Cyars, 1997 WL 33353409, at *3.
Third, Petitioner argues the Michigan court erroneously held he did not suffer any prejudice because the jury was instructed only to consider the “sworn testimony of witnesses,” which necessarily excludes statements the State used to impeach witnesses. This argument runs afoul of the well-established presumption jurors follow their instructions. See Penry v. Johnson, 532 U.S. 782, 799, 121 S.Ct. 1910, 150 L.Ed.2d 9 (2001). Fourth, Petitioner complains no evidence existed showing he planned to commit any crime against the victims, or that he had a “motive” for the killings, and some evidence corroborated his trial testimony. Petitioner’s final argument is flawed because evidence of “planning” and “motive” are not necessary to sustain a first-degree murder conviction under Michigan law. See Coddington, 470 N.W.2d at 487 (finding a “brief’ passage of time sufficient for the defendant to take a “second look”); People v. Herndon, 246 Mich.App. 371, 633 N.W.2d 376, 404 (2001) (explaining evidence of motive is not necessary to sustain a first-degree murder conviction).5
In short, Petitioner failed to carry his heightened AEDPA burden. See Mitchell v. Esparza, 540 U.S. 12, 124 S.Ct. 7, 12, 157 L.Ed.2d 263 (2003) (per curiam). He had the burden of demonstrating the Michigan court’s decision was objectively unreasonable, not that it may have applied Strickland incorrectly. See Visciotti, 537 U.S. at 27, 123 S.Ct. 357. Petitioner cannot carry his burden because the Michigan court’s conclusion that Petitioner did not suffer any prejudice is reasonable in light of the overwhelming circumstantial evidence of his guilt. No reasonable probability exists that but for counsel’s failure to proffer a limiting instruction on the proper use of impeachment statements the result of the trial would have been different. See Strickland, 466 U.S. at 696, 700, 104 S.Ct. 2052 (explaining trial errors are less likely to affect a verdict with “overwhelming record support”). As the Court recently explained, state courts have more leeway in reaching a particular outcome when they apply general rules of law. Alvarado, 124 S.Ct. at 2149. The Strickland test, by its nature, is general and not subject to mechanical application. Strickland, 466 U.S. at 696, 104 S.Ct. 2052; Kimmelman v. Morrison, 477 U.S. 365, 395, 106 S.Ct. 2574, 91 L.Ed.2d 305 (1986) (Powell, J., concurring). We therefore must defer' to the Michigan court’s reasonable conclusion that Petitioner did not suffer any prejudice as a result of his counsel’s failure to proffer a limiting instruction on the proper use of impeachment statements. The adversarial process clearly provided Petitioner with a fair trial. That is all the Sixth Amendment demands.
The Michigan court “considered the proper factors and reached a reasonable conclusion.” Alvarado, 124 S.Ct. at 2152. “That being the case, we may not set aside its decision on habeas review.” Esparza, 124 S.Ct. at 12.
AFFIRMED.
. The record does not disclose whether Petitioner exhausted his state court post-conviction remedies. See Mich. Ct. R. 6.500 to 6.509. The district court simply noted Petitioner filed his habeas application after exhausting his direct appeals. Petitioner's motion for a certificate of appealability similarly states his habeas application was filed after "exhausting his direct appeal rights.” We need not delve into the morass of procedural bar, however, because Petitioner’s claim fails *487on the merits even assuming he properly exhausted available state court remedies. See 28 U.S.C. § 2254(b)(2).
. Petitioner testified he was "scared” from the moment Taylor was to page Rob and Lucky. The record does not disclose, however, why Petitioner simply did not leave the house when Lewis was with Christon. In fact, Christon testified Lewis was not doing anything to keep Petitioner in the house.
. Petitioner testified on his own behalf at trial. Petitioner’s version of the events differed substantially from other evidence introduced at trial. Petitioner testified he shot Lewis because Lewis was going for another gun in his pants’ pocket. Other evidence at trial indicated, however, that Lewis’s hand was near his face when he was shot. Additionally, no other weapons were found on Lewis or in the house. Petitioner also testified he could not leave out of the house’s front door because the refrigerator was blocking the door. Petitioner explained that he attempted to move the refrigerator, but it got caught on the carpet. Petitioner thus believed his only other option was to leave through the window in Taylor’s room. When Petitioner entered Taylor’s room, however, she had a knife and went for a gun. Lumpkin, according to Petitioner's testimony, also had a gun. As noted, the police did not recover any such weapons. Petitioner nevertheless testified he shot Taylor and Lumpkin in self-defense. Petitioner admitted he thereafter left the Asbury House through its front door.
. AEDPA governs the habeas application Petitioner filed in 1999. See Garceau, 538 U.S. at 207, 123 S.Ct. 1398 (holding “an application filed after AEDPA’s effective date should be reviewed under AEDPA[.]”). AEDPA’s "contrary to” clause is inapposite because, as Petitioner admits, the Michigan court applied the correct governing law in rejecting his ineffective assistance of counsel claim. Cyars, 1997 WL 33353409, at *4 (citing People v. Pickens, 446 Mich. 298, 521 N.W.2d 797, 815 (1994) (adopting the Supreme Court's two-pronged test enunciated in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984) for analyzing ineffective assistance of counsel claims)). Furthermore, the Strickland analysis for evaluating ineffective assistance claims is "clearly established.” Wickline v. Mitchell, 319 F.3d 813, 819 (6th Cir.2003).
. We agree with Petitioner that some evidence corroborated his trial testimony. We also agree with counsel’s contention at oral argument that the impeachment statements were the only “direct evidence” of premeditation. These arguments are also irrelevant, however, because premeditation may be inferred from facts and circumstances established in the record. Coddington, 470 N.W.2d at 487.