
598 F.3d 416 (2010)
Terry C. BROWN, Petitioner-Appellant,
v.
Alan FINNAN, Respondent-Appellee.
No. 08-3151.
United States Court of Appeals, Seventh Circuit.
Argued October 30, 2009.
Decided March 17, 2010.
*419 Amanda A. Bennett (argued), Bethany N. Schols, Dykema, Chicago, IL, for Petitioner-Appellant.
Steve Carter, James B. Martin (argued), Office of the Attorney General, Indianapolis, IN, for Respondent-Appellee.
Before CUDAHY, POSNER, and ROVNER, Circuit Judges.
CUDAHY, Circuit Judge.
Having been convicted of murdering Charles Young, Jr. and Robert Hunter in 2000, Terry C. Brown was ultimately sentenced to serve two consecutive terms of 55 years. Brown subsequently filed a petition for post-conviction relief, claiming that he had received ineffective assistance of counsel at both the trial and appellate levels. His petition focused on an in-court announcement by one victim's mother to the effect that "the situation [was] racist" and her further proclamation on the courthouse steps that the courthouse should be treated similarly to the World Trade Center and bombed. Brown's attorney declined to request a hearing to determine the impact of these statements on the jury. Nor did his appellate counsel raise the issue on appeal. Brown now contends that his counsels' failure to address this issue violated the Sixth Amendment. He argues further that the Indiana courts' denial of his petition for post-conviction relief is contrary to well-established principles of federal law, as established by the U.S. Supreme Court in Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). He therefore asserts that this Court should grant his petition for a writ of habeas corpus.
We decline to do so. To prevail on an ineffective assistance of counsel claim under Strickland, a petitioner must demonstrate that his counsel's assistance was objectively unreasonable and resulted in a substantial risk of prejudice. Brown can meet neither requirement. The prejudicial impact of the statements here on the defendant's right to a fair trial is attenuated. Since both Brown and his victim, Young, were African-American, it is far from clear how a juror would perceive the assertion of racism in a manner necessarily injurious to Brown. While obviously serious, a distraught parent's threat of bombing the courthouse does not obviously bear on the guilt or innocence of the defendant. Moreover, there is no evidence that *420 this out-of-court statement was heard by any juror. Finally, though no less important, there may be good reason not to draw explicit attention to such statements. Apt counsel might conclude that her client's cause would best be promoted by not focusing on issues of tenuous significance to her client's guilt or innocence. For these reasons, Brown's counsels' performance was not objectively unreasonable. Nor did his attorneys' conduct result in a substantial risk of prejudice. For these reasons, and the reasons that follow, we deny Brown's petition.

I. BACKGROUND
On the afternoon of July 16, 2000, two police officers on bike patrol heard gunfire and shortly thereafter observed Terry C. Brown run into and then hastily depart a barbershop. Brown was carrying a white document and an unidentified object under his arm. After the officers discovered Charles Young, Jr. lying on the ground with a gunshot wound in his neck, they split up. One officer gave chase and successfully apprehended Brown. The other entered the barbershop and found Robert Hunter, who had been shot in the head.
When arrested, Brown had blood on his clothing, though he did not have possession of the item with which he had been seen exiting from the barbershop. An ensuing search of the immediate area uncovered a gun sight and a white piece of paper, in addition to a bag, which contained a .38-caliber revolver and a 9mm semiautomatic. One of the firearms had six empty shell casings in it, while the other was loaded with a round in the chamber and one round missing. The paper appeared to have blood on it.
On the same day he was arrested, Brown was charged with the murder of Young and Hunter. Two instances of note occurred during his ensuing trial. During the State's presentation of evidence, Corey Young, the mother of victim Charles Young, Jr., announced from the gallery that "the situation [was] racist." Although Brown and his attorney noticed the remark, the judge did not hear it and testimony continued without interruption. Brown's attorney did not bring the matter to the court's attention. It is unclear whether any juror perceived Ms. Young's statement.
The second incident occurred the same day on the courthouse steps. Ms. Young apparently stated that "this courthouse should be treated similar to the World Trade Center and the whole place should be bombed." There is no evidence that any juror was privy to this remark.
When apprised of these statements, and outside the presence of the jury, the trial judge impressed upon the spectators in the gallery that he would not tolerate such comments. He dismissed Ms. Young from the remainder of the trial. The trial judge did not take any further action, such as holding a hearing to determine the effect, if any, of the statements on the jury. Neither the defense counsel nor the prosecutor requested such a course of action. The rest of the trial proceeded without incident.
On September 19, 2001, the jury found Brown guilty of both murders. Consistent with the jury's recommendation, the trial court sentenced him to two concurrent sentences of life in prison without parole. On appeal, the Indiana Supreme Court remanded the case for resentencing. On remand, the trial court imposed the same sentence. Brown again appealed to the Supreme Court of Indiana. Finding the trial court's sentencing order to be inadequate, the Indiana Supreme Court ordered a remand with instructions to impose two consecutive sentences of 55 years. Brown *421 v. State, 783 N.E.2d 1121, 1126-29 (Ind. 2003). On neither appeal did Brown's attorney raise the court's failure to hold a hearing to consider the impact of Ms. Young's statements on the jury.
On January 2, 2004, Brown filed a pro se petition for post-conviction relief, which he amended on August 21, 2006. In pertinent part for our consideration, Brown's petition provided that he was denied effective assistance of both trial and appellate counsel. He contended that his trial counsel failed to act as counsel guaranteed by the Sixth Amendment due to his failure to request a hearing following Ms. Young's comments. He argued that his appellate attorney's performance was similarly deficient for not raising this issue on appeal. Brown further asserts that both counsels' deficient performances resulted in prejudice.
The Howard County Circuit Court denied Brown's petition for post-conviction relief, finding that Brown could only speculate as to whether any juror actually heard Ms. Young's comments. It also found that it was unclear what her in-court remark even referred to. The Indiana Court of Appeals affirmed. Brown v. State, 874 N.E.2d 651, 2007 WL 2917084 (Ind.App. Oct.9, 2007). In applying the Strickland standard, which requires a showing of both deficient performance and prejudice, the appellate court declined to examine whether Ms. Young's out-of-court statement was prejudicial because there was no showing that any juror either heard the remark or was made aware of it. Expressing skepticism as to whether any juror heard Ms. Young's in-court remark, the Indiana Court of Appeals also observed a lack of evidence pertaining to the statement's prejudicial effect. This being the case, the court expressed doubt whether the trial court would have granted a request for a hearing.
Brown then filed a petition for a writ of habeas corpus with the United States District Court for the Southern District of Indiana. Since the district court found that the Indiana Court of Appeals correctly recognized and applied the Strickland standard, it denied Brown's petition. We granted his motion for a certificate of appealability on September 30, 2008. Brown now appeals the decision of the district court not to grant his petition for a writ of habeas corpus. For the reasons explained below, we affirm.

II. DISCUSSION
The standard by which we review a state court's decision on a federal constitutional issue is a familiar one. Under the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"), we may grant habeas relief only if the state's adjudication of the issue: (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 or (2) resulted in a decision that 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). We review the decision of the last state court to review the issue. See Lucas v. Montgomery, 583 F.3d 1028, 1030 (7th Cir. 2009).
For the purposes of habeas corpus review, "[c]learly established federal law" means "the governing principle or principles set forth by the Supreme Court at the time the state court renders its decision." Lockyer v. Andrade, 538 U.S. 63, 71-72, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003). A state-court decision is "contrary to" federal law if the state court either erroneously laid out governing U.S. Supreme Court precedent, or, having identified the correct rule of law, decided a case *422 differently than a materially factually indistinguishable Supreme Court case. 28 U.S.C. § 2254(d)(1); Sutherland v. Gaetz, 581 F.3d 614, 616 (7th Cir.2009). An "unreasonable application" of U.S. Supreme Court precedent occurs when a state court identifies the correct governing legal rule but unreasonably applies it to the facts of a case or if the state court either unreasonably extends a legal principle from the Supreme Court's precedent to a new context in which it should not apply or unreasonably refuses to extend that principle to a new context in which it should apply. Gaetz, 581 F.3d at 616.
Whether a state ruling runs afoul of these AEDPA standards is a legal determination, and, as such, we review the district court's determination de novo. See Sweeney v. Carter, 361 F.3d 327, 330 (7th Cir.2004); see also Gaetz, 581 F.3d at 616. However, we review the district court's factual determinations for clear error. See Smith v. Grams, 565 F.3d 1037, 1043 (7th Cir.2009).

A. The State Court Correctly Determined That Petitioner Did Not Receive Ineffective Assistance of Trial Counsel
Brown contends that he received ineffective assistance of counsel, in violation of the Sixth Amendment, because his trial attorney failed to request a hearing in light of Ms. Young's two statements. To prevail, Brown "must show that counsel's performance was deficient, and that the deficiency prejudiced the defense." Wiggins v. Smith, 539 U.S. 510, 521, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (citing Strickland, 466 U.S. at 687, 104 S.Ct. 2052). To demonstrate this deficiency, he "must show that counsel's representation fell below an objective standard of reasonableness." Strickland, 466 U.S. at 688, 104 S.Ct. 2052; Wiggins, 539 U.S. at 521, 123 S.Ct. 2527. That objective standard of reasonableness, in turn, is determined by prevailing professional norms. Strickland, 466 U.S. at 688, 104 S.Ct. 2052. "We assess counsel's work as a whole, and `it is the overall deficient performance, rather than a specific failing, that constitutes the ground of relief.'" Pole v. Randolph, 570 F.3d 922, 934 (7th Cir.2009) (citing Peoples v. United States, 403 F.3d 844, 848 (7th Cir.2005)). "The bar for establishing that a state court's application of the Strickland standard was `unreasonable' is a high one, and only a clear error in applying Strickland will support a writ of habeas corpus." Allen v. Chandler, 555 F.3d 596, 600 (7th Cir.2009).
Brown grounds his claim of ineffective assistance of trial counsel on the latter's election not to request a hearing to determine the effect of Ms. Young's in-court and out-of-court statements. We consider each statement in turn.

A. Ms. Young's In-Court Statement

Would an objectively reasonable attorney necessarily request a hearing in light of Ms. Young's proclamation from the gallery that "the situation is racist"? We do not believe so. Given that the victim, Charles Young, Jr. and the accused were both African-American, the meaning of the challenged statement is equivocal. It is not at all clear how a jury would perceive the assertion in a manner injurious to Brown. Were a juror to interpret the remark as implying that the trial were biased against the defendant due to this race, this would seem to be a boon to Brown. But to the extent a juror viewed the comment as reflecting on the treatment given Young by the authorities, then the statement was wholly irrelevant to Brown's guilt or innocence. Notably, Brown himself speculated on cross-examination that Ms. Young was expressing her *423 displeasure at the police department's treatment of her son. Under either interpretation, Ms. Young's statement that the situation was racist is ambiguous and apparently innocuous.
Faced with such a remark, which the jury may or may not have heard, it would be entirely reasonable for counsel to elect not to pursue the matter. An able attorney might well conclude that his client's cause would best be served by not drawing the jury's attention to issues that are largely, if not completely, irrelevant to his client's guilt or innocence. We cannot find that Brown's trial attorney acted unreasonably, particularly in light of the fact that we adopt "a strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance." Strickland, 466 U.S. at 689, 104 S.Ct. 2052.
Brown seeks to escape this conclusion by characterizing Ms. Young's comment as extraneous and contending that the Supreme Court's holding in Remmer v. United States thus compels a hearing. 347 U.S. 227, 229, 74 S.Ct. 450, 98 L.Ed. 654 (1954). Brown overstates the reach of the Court's decision in Remmer. In that case, a juror was told by an unnamed person that he could profit by finding for the petitioner. The district court denied a motion for a new trial and the Court of Appeals affirmed, finding that the petitioner had not demonstrated prejudice. The Supreme Court reversed, holding:
In a criminal case, any private communication, contact, or tampering directly or indirectly, with a juror during a trial about the matter pending before the jury is, for obvious reasons, deemed presumptively prejudicial, if not made in pursuance of known rules of the court and the instructions and directions of the court made during the trial, with full knowledge of the parties.
Remmer, 347 U.S. at 229, 74 S.Ct. 450. Assuming that the jury in fact heard Ms. Young's in-court remark, Remmer raises an important question: did her statement constitute the kind of unauthorized contact that triggers a presumption of prejudice and thus requires a hearing? The respondent contends that the utterance lacks the private nature of the communication present in Remmer and therefore does not compel a hearing. There is some force to this suggestion, given the Supreme Court's reference to any "private" communication. We note, however, that at least one prior decision of this Court might be read to suggest otherwise. See Evans v. Young, 854 F.2d 1081, 1082-84 (7th Cir.1988) (suggesting that an in-court statement made within earshot of the jury can require a Remmer hearing, even if the comment were not made in private).
Regardless, Ms. Young's assertion did not necessitate a Remmer hearing. This is because the comment was not one that would affect a reasonable juror's deliberation as to whether Brown was guilty or innocent. See Whitehead v. Cowan, 263 F.3d 708, 724-25 (7th Cir.2001). Brown appeals to an excessively literal interpretation of the Supreme Court's pronouncement that "any private communication . . . with a juror during a trial" is deemed prejudicial. The relevant communication must, of course, be read in its context (and the content of the communication might not be known if it were in fact completely "private"). See Wisehart v. Davis, 408 F.3d 321, 326 (7th Cir.2005). In this respect, we have repeatedly held that no Remmer hearing is necessary when the challenged statement is both ambiguous and innocuous. See Whitehead, 263 F.3d at 724-25; see also United States v. Al-Shahin, 474 F.3d 941, 949 (7th Cir.2007). As we have explained above, Ms. Young's statement can be so characterized.
*424 Therefore, no Remmer hearing was necessary in light of Ms. Young's in-court remark and it was reasonable for Brown's attorney to elect not to request one. See also United States v. Gallardo, 497 F.3d 727, 736 (7th Cir.2007) ("In order for a hearing to be required, `the extraneous communication to the juror must be of a character that creates a reasonable suspicion that further inquiry is necessary to determine whether the defendant was deprived of his right to an impartial jury.'") (quoting Wisehart v. Davis, 408 F.3d 321, 326 (7th Cir.2005)).
In light of the above, we have little trouble finding that Brown's trial attorney's performance did not fall below an objective standard of reasonableness. For much the same reason, we also find that Brown cannot establish prejudice. The challenged statement is ambiguous and innocuous. In addition, the evidence against Brown seems strong. Even putting aside the questions of whether the jury even heard the remark and construed it in a prejudicial way, the inculpatory evidence detracts from his contention that Ms. Young's statement undermines confidence in the outcome of the trial. See, e.g., Whitehead, 263 F.3d at 724 ("Finally, the evidence of defendant's guilt was overwhelming, and this `militates against a finding that the introduction of the disputed [material] affected the jury's verdict.'") (citing United States v. Paneras, 222 F.3d 406, 411 (7th Cir.2000)).
The state court's conclusion that Brown received effective assistance of counsel did not, then, constitute an unreasonable application of federal law, as established by the Supreme Court. Nor did it amount to an unreasonable determination of the facts in light of the evidence presented in the state-court proceeding.

B. Ms. Young's Out-of-Court Statement

We now move to consider Ms. Young's more serious, out-of-court statement that the courthouse should be treated similarly to the World Trade Center and ought to be bombed. The state court declined to consider whether this declaration presented a risk of prejudice because Brown had made no showing that any juror heard or was made aware of Ms. Young's out-of-court proclamation. Brown v. State, 874 N.E.2d 651, at *4 (2007) (citing Worthington v. State, 273 Ind. 499, 405 N.E.2d 913, 916 (Ind.1980), cert. denied, 451 U.S. 915, 101 S.Ct. 1991, 68 L.Ed.2d 306 (1981) ("Absent a basis for believing that the jury may have been subjected to improper out-of-court stimuli, there is no need to employ the procedure outlined in Lindsey.")).
The state court's conclusion in this regard was not contrary to, nor did it involve an unreasonable application of, clearly established federal law, as established by the U.S. Supreme Court. Indeed, the state court's finding, which was based on Brown's failure to introduce evidence that a juror perceived the comments, finds support in several decisions of the U.S. courts of appeals. These decisions suggest the absence of a clearly established federal law to the contrary. See, e.g., United States v. Davis, 15 F.3d 1393, 1412 (7th Cir.1994) (observing that "[o]nce a defendant had made a sufficient showing that a juror may have been improperly influenced, the court must ascertain whether the juror was or was not tainted") (emphasis in original); United States v. Rosales, 680 F.2d 1304, 1306 (10th Cir.1981) (no abuse of discretion to decline to hold a hearing where there was no evidence that any juror other than the one discharged heard the extraneous remarks); United States v. Schoppert, 362 F.3d 451, 459 (8th Cir.2004) ("A defendant must, moreover, make some effort to support an allegation of jury taint *425 before an evidentiary hearing or declaration of a mistrial will be appropriate. A bald assertion of taint will not suffice; the defendant needs to make a showing that his allegation is credible and that the prejudice alleged is serious enough to warrant whatever action is requested."); King v. Bowersox, 291 F.3d 539, 541 (8th Cir.), cert. denied, 537 U.S. 1093, 123 S.Ct. 693, 154 L.Ed.2d 641 (2002) (finding no need to embark on a Remmer analysis in the absence of a showing that the jury saw or was aware of hallway display in memory of victim).
Here, Brown does not even allege that a juror was privy to Ms. Young's remarks on the courthouse steps. Rather, he merely alleges that a juror could have heard her statement outside the courthouse. This is an insufficient basis for establishing that a Remmer hearing must be conducted. Therefore, the Indiana Court of Appeals' election not to countenance Brown's claim of prejudice was not inconsistent with, nor did it involve an unreasonable application of, clearly established federal law.
Assuming, arguendo, that there were some modicum of evidence that a juror heard Ms. Young's threat to the courthouse, it is not clear that the remark would have prejudiced Brown. Although evidently an abhorrent remark, particularly in the days following the attacks of 9/11, it would not seem to weigh on Brown's perceived guilt or innocence in the eyes of the jury. As in Whitehead, "[t]he mother did not attempt to persuade the jury, nor did she provide them with any extraneous information about the facts of the case. . . . While understandably emotional, the statement was not prejudicial." 263 F.3d at 724. In short, stating that the courthouse should be bombed does not readily translate into an aspersion on the defendant. It is therefore akin to the kind of ambiguous and innocuous remark that does not require a Remmer hearing. Id. at 724-25.

B. The State Court Correctly Determined That Petitioner Did Not Receive Ineffective Assistance of Appellate Counsel
Brown also contends that he received ineffective assistance of appellate counsel. As should be clear from the preceding discussion, Ms. Young's statements were not of the kind that would warrant an inference of prejudice. Nor is there evidence that any juror was privy to Ms. Young's out-of-court statement. Just as it was reasonable for Brown's trial attorney not to request a hearing, so was it reasonable for his appellate attorney to focus on issues of import to the jury's guilty verdict and the trial court's imposed sentence.
Appellate counsel's performance is similarly measured against that of an objectively reasonable attorney. See Lee v. Davis, 328 F.3d 896, 900 (7th Cir. 2003). An appellate counsel's performance is deficient if she fails to argue an issue that is both obvious and clearly stronger than the issues raised. Martin v. Evans, 384 F.3d 848, 851 (7th Cir.2004) (citing Lee v. Davis, 328 F.3d 896, 900-01 (7th Cir. 2003)). However, counsel is not required to raise every nonfrivolous issue on appeal. Martin, 384 F.3d at 852 (citing Mason v. Hanks, 97 F.3d 887, 893 (7th Cir.1996)).
To prevail, Brown must show that there is a reasonable probability that the issue his appellate attorney failed to raise would have altered the outcome of the appeal, had it been raised. Lee, 328 F.3d at 901. Petitioner cannot make such a showing and his petition must fail accordingly.
There is no evidence that any juror heard Ms. Young's threatening remarks outside the courthouse. Even if *426 there were such evidence, those threats were directed at the courthouse and did not cast an aspersion of guilt on the defendant. Ms. Young's in-court assertion that the situation was racist was ambiguous and innocuous, given the context within which the remark was made. This being the case, there was no need for a hearing and reasonable appellate counsel could wisely disregard Ms. Young's statements in favor of issues that weigh on Brown's guilt and sentence. Although Brown offers Oswald v. Bertrand, in support of his position, that case simply provides that "the greater [the] probability [of bias], the more searching the inquiry needed to make reasonably sure that an unbiased jury is impaneled." 374 F.3d 475, 480 (7th Cir.2004). In the present case, evidence of bias is limited to the point of being nonexistent. This being the case, Oswald supports the decision of Ward's appellate counsel not to raise the trial court's failure to hold a hearing.
The Indiana Court of Appeals correctly held that, because Ms. Young's statements did not present a substantial risk of prejudice, Brown could not establish that his appellate attorney's performance was deficient.

III. CONCLUSION
The Indiana Court of Appeals' finding that Brown received effective assistance of trial and appellate counsel was not contrary to, nor did it involve an unreasonable application of, clearly established federal law, as established by the U.S. Supreme Court. Nor was its finding based on an unreasonable determination of the facts. The in-court statement of one victim's mother to the effect that the situation was racist was ambiguous in its import and, in any event, innocuous. Her out-of-court proclamation that the courthouse should be bombed was of course more serious. Yet, even this assertion bears no obvious relevance to the question of the defendant's innocence or guilt. More important still, Brown has failed to provide even a scintilla of evidence that any juror was privy to this remark. The judgment of the district court is therefore
AFFIRMED.
