
537 F.3d 466 (2008)
Patrick Timothy RICHARDSON, Petitioner-Appellant,
v.
Nathaniel QUARTERMAN, Director, Texas Department of Criminal Justice, Correctional Institutions Division, Respondent-Appellee.
No. 06-10872.
United States Court of Appeals, Fifth Circuit.
July 28, 2008.
*468 Gary Alan Udashen (argued), Sorrels, Udashen & Anton, Dallas, TX, for Petitioner-Appellant.
Jon R. Meador (argued), Postconviction Litigation Div., Austin, TX, for Respondent-Appellee.
Before JONES, Chief Judge, and GARWOOD and JOLLY, Circuit Judges.
GARWOOD, Circuit Judge:
Petitioner-Appellant, Patrick Timothy Richardson (Richardson), a Texas prisoner, pleaded guilty in a Texas court to the murder of his wife, Mary Richardson. The wife of the trial judge who presided in his case was an acquaintance of Mary Richardson. Thus, before his trial, Richardson filed a motion to recuse the trial judge. Following a pretrial hearing, an assigned administrative judge denied this motion. After unsuccessfully appealing his conviction in state court and filing a state habeas application, Richardson filed an application for a federal writ of habeas corpus under 28 U.S.C. § 2254 arguing, inter alia, that the trial judge should have been recused from his case. The district court denied Richardson's petition for habeas relief and Richardson now appeals its decision. For the following reasons, we affirm the judgment of the district court.

FACTS AND PROCEEDINGS BELOW
On March 29, 2000, Richardson was indicted in Dallas County, Texas, for the September 19, 1999 murder of his wife, Mary Richardson. Immediately after the murder, Judge King set the bond in Richardson's case. However, the case was assigned to Judge Henry Wade, Jr. a few days later, on Thursday, September 23. On Friday, September 24, 1999, Richardson made a motion in the trial court to recuse Judge Henry Wade, Jr., claiming that the judge's impartiality might reasonably be questioned because his wife, Judge Kristin Wade, was an acquaintance of the murder victim. Both Judge Henry Wade, Jr. and Judge Kristin Wade testified regarding their connections to Mary Richardson in a recusal hearing held in the state trial court on October 8, 1999. Judge Pat McDowell, the presiding administrative judge who conducted the recusal hearing, denied Richardson's request to recuse Judge Henry Wade, Jr.
At the time of Mary Richardson's death, Judge Kristin Wade was a member of the Junior League of Dallas (the Junior *469 League), a volunteer organization with approximately 5,600 members, all Dallas area women. Both she and Mary Richardson served on the Junior League leadership council, which consisted of approximately forty or forty-two members, and met seven or eight times between June 1, 1998 and May 31, 1999, the Junior League's administrative year before Mary Richardson's death.
At the recusal hearing, Judge Kristin Wade testified that she would classify Mary Richardson as more of an acquaintance than a friend, and that their conversations generally centered around Junior League business. She did not know personal details about Mary Richardson, such as the number or names of her children. Furthermore, neither she nor her husband, who are elected judges, received campaign contributions from the deceased. Judge Kristin Wade also testified that she worked with Mary Richardson at leadership counsel meetings on at least a few occasions. On December 6, 1998, the two women also attended a party at the house of Connie O'Neil, the president of the Junior League at that time. Judge Henry Wade, Jr. attended this party with his wife, and Richardson most likely also attended with Mary Richardson. Judge Kristin Wade testified that both she and her husband most likely met the Richardsons at this party. Judge Kristin Wade testified she had never been to the Richardson home and Mrs. Richardson had never been to her home.
Within a day of when Richardson was arrested for the murder of his wife on Sunday, September 19, 1999, he was released on a $30,000 bond set by Judge King. Judge Kristin Wade testified that the day after the murder, Monday, September 20, 1999, she discussed Richardson's bond with her husband on the way to work. She denied that they discussed whether the bond amount was set too high or low, although she did admit that at some point, she told her husband that she disapproved of the amount of Richardson's bond. That Monday and Tuesday, about five or six members of the Junior League called Judge Kristin Wade regarding the murder. Several of these callers indicated that they thought Richardson should not be out on bond and that the bond was set too low. On one of those days, Judge Kristin Wade contacted Judge King and an assistant district attorney involved in the case to seek information regarding the bond so that she could answer the callers' questions and know whom she should tell them to contact with their concerns.
On Wednesday, September 22, 1999, Judge Kristin Wade also attended Mary Richardson's funeral and a reception following the funeral at the headquarters of the Junior League. While she first testified that the general consensus at the reception was outrage that Richardson was out on bond, she later stated that, "[she] really [did not] know that there was much bond conversation at all at that particular reception." After Judge Henry Wade, Jr. was assigned the case on Thursday, September 23, 1999, Judge Kristin Wade called Junior League headquarters, and spoke with Connie O'Neil and maybe one other woman to tell them that no one should call her regarding Richardson because she could no longer discuss the case.
Before he was assigned the case, Judge Henry Wade, Jr. knew of the phone calls his wife had received from Junior League members who were unhappy about Richardson's bond. He was also aware that his wife knew Mary Richardson through the Junior League and that she had attended both her funeral and the following reception at the Junior League. He testified that he did not know either the deceased or Richardson, and that he would not be *470 biased or influenced by the fact that the deceased had been a member of the Junior League with his wife. There is no evidence that Judge Henry Wade, Jr. had ever been in the Richardson home or that either Richardson had ever been in the Wade home.
Other than outlined above, there is no evidence of any relationship or connection between either Richardson and either Wade.
On Tuesday, September 21, 1999, before Judge Henry Wade, Jr. was assigned the case, the district attorney's office presented to him a motion to hold Richardson's bond insufficient. The Thursday morning that the case was assigned to him, Judge Henry Wade, Jr. raised the amount of Richardson's bond from $30,000 to $1,000,000 without a hearing and in the absence of Richardson's counsel.
After September 24, 1999, and before trial, Richardson filed a motion to recuse Judge Henry Wade, Jr. Judge Pat McDowell, an administrative judge, held a recusal hearing on October 8, 1999, and denied Richardson's request to recuse. Trial was held in May 2000. At trial, Richardson pleaded guilty, to a jury, to the murder of his wife. After hearing evidence at a trial on punishment the jury convicted Richardson of murder, and assessed him a sentence of sixty years confinement and a fine of $10,000.
On Richardson's direct appeal, he argued, inter alia, that Judge Henry Wade, Jr. was biased and should have been recused because his wife knew the deceased. On August 1, 2002, a Texas appellate court affirmed Richardson's conviction. Richardson v. State, 83 S.W.3d 332, 362 (Tex.App.  Corpus Christi 2003, pet. ref'd). It applied the recusal standard set forth in Texas case law, and held that the trial court should have recused Judge Henry Wade, Jr. because the "undisputed evidence" (as outlined by the court of appeals) at the recusal hearing demonstrated that "a reasonable member of the public, knowing all the circumstances involved, would have questions or doubts as to the impartiality of the trial judge." See id. at 358-59 (citing Sears v. Nueces County, 28 S.W.3d 611, 615 (Tex.App.Corpus Christi 2000, no pet.) and Woodruff v. Wright, 51 S.W.3d 727, 738 (Tex.App.Texarkana 2001, pet. denied)). The court of appeals also noted that it did not find "that there was any actual bias, prejudice, or partiality on the part of Judge Henry Wade Jr." Id. at 359. Finally, the court went on to hold that the failure to recuse Judge Henry Wade, Jr. was harmless error under Texas Rule of Appellate Procedure 44.2. Id. at 360.[1] The court of appeals denied Richardson's *471 petition for rehearing of its decision, and the Texas Court of Criminal Appeals refused Richardson's petition for discretionary review.
Richardson filed a state habeas application on December 22, 2003, arguing, inter alia, that the Texas court of appeals improperly engaged in harmless error analysis and that, in the alternative, the error was not harmless. The state filed a response to this application arguing that Richardson's habeas application should be denied. Richardson also filed a motion requesting that Judge Henry Wade, Jr. be recused from the habeas proceedings, which the trial court granted in an Order of Recusal on February 9, 2004. On February 17, 2004, the trial court denied Richardson's state habeas application, finding that "there [were] no controverted, previously unresolved facts material to the legality of the [Richardson's] confinement which require[d] an evidentiary hearing." Thus, no additional evidentiary hearing was conducted. The Texas Court of Criminal Appeals denied the application without written order on March 31, 2004.
On June 28, 2004, Richardson, proceeding with counsel, filed the instant application for writ of habeas corpus under 28 U.S.C. § 2254. He argued, inter alia, that the state appellate court incorrectly applied harmless error analysis, and that its finding that "a reasonable member of the public, knowing all the circumstances involved, would have questions or doubts as to the impartiality" of Judge Henry Wade, Jr. amounted to constitutional structural error, which should have resulted in automatic reversal. See Richardson, 83 S.W.3d at 358-59. He also argued that the error was not harmless and that Judge Henry Wade, Jr. was actually biased.
On June 29, 2006, the magistrate judge (MJ) recommended that the district court deny Richardson's petition. The MJ determined first that Richardson failed to show that the trial judge was actually biased against him. The MJ also found that the federal due process standard for recusal was narrower than the state recusal standard applied by the Texas court of appeals. Therefore, the MJ concluded that the Texas court of appeals' finding of the appearance of bias was not entitled to deference. The MJ also concluded that, under the federal standard, there was no appearance of bias sufficient to violate the Due Process Clause, so Richardson failed to show that his trial fell within the limited class of cases representing structural error.
Over Richardson's objections, the district court adopted the MJ's recommendation and denied Richardson's petition for habeas relief on July 26, 2006. Richardson timely appealed on August 15, 2006. This court granted Richardson a certificate of appealability (COA) "on the issue whether the appearance of bias in a trial judge amounts to structural error and whether the state appellate court's conclusion here that a reasonable person could question the trial judge's impartiality necessarily included a finding of a due process violation that should have been afforded deference."

DISCUSSION
We limit our discussion to the issues approved in the COA: (1) Whether the appearance of bias in a trial judge is a structural error that requires automatic reversal, and (2) whether the state appellate court's conclusion that Judge Henry *472 Wade, Jr. appeared to be biased necessarily included a factual finding of a due process violation that this court should afford deference.[2] For the reasons stated below, we affirm the judgment of the district court.

A. Jurisdiction and Standard of Review
This court has jurisdiction over this habeas corpus proceeding pursuant to 28 U.S.C. § 2253(a) and (c)(1)(A). In a federal habeas corpus appeal, the district court's findings of fact are reviewed for clear error, while its conclusions of law are reviewed de novo. Buntion v. Quarterman, 524 F.3d 664, 670 (5th Cir.2008). Because Richardson's federal petition for habeas review was filed after 1996, the district court applied the Antiterrorism and Effective Death Penalty Act (AEDPA). Under the pertinent AEDPA provision, 28 U.S.C. § 2254(d), a federal court may only grant a state prisoner's application for a writ of habeas corpus if his incarceration was the product of a state court adjudication that:
"(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."
This court reviews questions of law and mixed questions of law and fact under section 2254(d)(1), while it reviews questions of fact under section 2254(d)(2). Horn v. Quarterman, 508 F.3d 306, 312 (5th Cir.2007) (citing Martin v. Cain, 246 F.3d 471, 475 (5th Cir.2001)). The parties do not dispute the pertinent facts pertaining to Judge Henry Wade, Jr.'s interest in the case. Instead, they dispute whether, in light of these facts, Richardson's due process rights were violated. Thus, whether Richardson's due process rights were violated is a question of law, and should be evaluated under section 2254(d)(1).
The phrase "clearly established Federal law" for the purposes of 28 U.S.C. § 2254(d)(1) refers to "the governing legal principle or principles set forth by the Supreme Court at the time the state court render[ed] its decision." Lockyer v. Andrade, 538 U.S. 63, 123 S.Ct. 1166, 1172, 155 L.Ed.2d 144 (2003) (quoting Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)). It includes the holdings, but not the dicta, of these Supreme Court opinions. Id.
A state court "decision is contrary to clearly established federal law `if the state court arrives at a conclusion opposite to that reached by [the Supreme Court] on *473 a question of law or if the state court decides a case differently than [the] Court has on a set of materially indistinguishable facts.'" Gardner v. Johnson, 247 F.3d 551, 557 (5th Cir.2001) (alterations in original) (quoting Williams, 120 S.Ct. at 1523). Further, as we said in Horn, 508 F.3d at 312-13:
"A state court's decision constitutes an `unreasonable application' of `clearly established Federal law, as determined by the Supreme Court,' `"if the state court correctly identifies the governing legal principle from [Supreme Court] decisions but unreasonably applies it to the facts of the particular case."' Busby [v. Dretke], 359 F.3d [708,] 713 [5th Cir. 2004] (quoting Bell v. Cone, 535 U.S. 685, 694, 122 S.Ct. 1843, 152 L.Ed.2d 914 (2002)). `We cannot reverse the denial of habeas relief simply by concluding that the state court decision applied clearly established federal law erroneously,' but rather, `we must conclude that such application was also unreasonable.' Martin [v. Cain], 246 F.3d [471] 476 [5th Cir.2001]; see Neal v. Puckett, 286 F.3d 230, 233 (5th Cir.2002) (en banc) (per curiam) (denying habeas relief where state court's conclusion was incorrect but not unreasonable)." (footnote omitted)
As the Supreme Court recently noted in Wright v. Van Patten, ___ U.S. ___, 128 S.Ct. 743, 743, 169 L.Ed.2d 583 (2008), "Because our cases give no clear answer to the question presented ... `it cannot be said that the state court "unreasonabl[y] appli[ed] clearly established Federal law."'" (quoting Carey v. Musladin, 549 U.S. 70, 127 S.Ct. 649, 654, 166 L.Ed.2d 482 (2006)).
A State court's findings of fact are presumed to be 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). We defer to a state court's findings of fact "unless they were based on an unreasonable determination of the facts in light of the evidence presented in the state court proceeding." Gardner, 247 F.3d at 557 (internal quotations and citations omitted); see also Buntion, 524 F.3d at 670. In this case, we defer to the pertinent undisputed facts outlined in the opinion of the Texas court of appeals, though we will not draw inferences beyond these facts. See Richardson, 83 S.W.3d at 354-58.
Finally, under section 2254(d)(2), this court should review the "ultimate decision" of the Texas courts, not "every jot of [their] reasoning." Santellan v. Cockrell, 271 F.3d 190, 193 (5th Cir.2001). Thus, instead of focusing on the reasoning of state courts in denying Richardson relief, we will focus on the outcome of their decisions.

B. Appearance of Bias
Richardson argues that Judge Henry Wade, Jr. appeared to be biased, and that an appearance of bias in a trial judge is a "structural error," a constitutional error subject to automatic reversal without the use of harmless error review. Neder v. United States, 527 U.S. 1, 119 S.Ct. 1827, 1833, 144 L.Ed.2d 35 (1999). Structural errors occur only in a very small class of cases, such as when a trial judge is actually biased. Id. (citing Tumey v. Ohio, 273 U.S. 510, 47 S.Ct. 437, 71 L.Ed. 749 (1927)). Richardson contends that, under Supreme Court precedent, both actual bias and the appearance of bias in a trial judge constitute structural errors because they both violate a defendant's due process rights. Thus, Richardson argues, the Texas court of appeals improperly applied harmless error review after finding that the trial court erred in refusing to recuse Judge Henry Wade, Jr.
*474 Under 28 U.S.C. § 2254(d)(1), we may grant Richardson's application for a writ of habeas corpus only if his incarceration was the product of a state court adjudication that violated his clearly established rights under the Due Process Clause as they are set forth in Supreme Court precedent.[3]Buntion, 524 F.3d at 671 (holding that the district court erred by relying on sources outside of clearly established Supreme Court precedent and by evaluating the state judge's behavior under the Texas Code of Judicial Conduct). Richardson has not alleged a violation of any other right, and we do not have jurisdiction to determine his rights under federal or state recusal statutes or ethical canons as such.[4]
Under the Due Process Clause, a criminal defendant is guaranteed the right to a fair and impartial tribunal. Bracy v. Gramley, 520 U.S. 899, 117 S.Ct. 1793, 1797, 138 L.Ed.2d 97 (1997). The Due Process Clause "establishes a constitutional floor, not a uniform standard." Id. This floor requires a fair trial, "before a judge with no actual bias against the defendant or interest in the outcome of his particular case." Id. (citation omitted).
However, "bias by an adjudicator is not lightly established." Valley v. Rapides Parish Sch. Bd., 118 F.3d 1047, 1052 (5th Cir.1997). Courts ordinarily "presume that public officials have properly discharged their official duties." Bracy v. Gramley, 117 S.Ct. at 1799 (internal quotation marks and citations omitted). General allegations of bias or prejudice are insufficient to establish a constitutional violation. See Aetna Life Ins. Co. v. Lavoie, 475 U.S. 813, 106 S.Ct. 1580, 1585, 89 L.Ed.2d 823 (1986) (holding that general allegations of a judge's frustration with insurance companies are not sufficient to force recusal under the Due Process Clause from a case in which an insurance company was a party). The Supreme Court has stated that "most matters relating to judicial disqualification [do] not rise to a constitutional level." Id. at 1584 (quoting FTC v. Cement Inst., 333 U.S. 683, 68 S.Ct. 793, 804, 92 L.Ed. 1010 (1948)). So even if a *475 judge is disqualified under state or federal law, the disqualification is not always required by the Due Process Clause. See id. at 1585.
In general, the Supreme Court has recognized "presumptive bias" as the one type of judicial bias other than actual bias that requires recusal under the Due Process Clause. Buntion, 524 F.3d at 672. Presumptive bias occurs when a judge may not actually be biased, but has the appearance of bias such that "the probability of actual bias ... is too high to be constitutionally tolerable." Id. (quoting Withrow v. Larkin, 421 U.S. 35, 95 S.Ct. 1456, 1464, 43 L.Ed.2d 712 (1975)). The Supreme Court has only found that a judge's failure to recuse constitutes presumptive bias in three situations: (1) when the judge "has a direct personal, substantial, and pecuniary interest in the outcome of the case," (2) when he "has been the target of personal abuse or criticism from the party before him," and (3) when he "has the dual role of investigating and adjudicating disputes and complaints."[5]Buntion, 524 F.3d at 672 (quoting Bigby v. Dretke, 402 F.3d 551, 559 (5th Cir.2005)); see also Crater v. Galaza, 491 F.3d 1119, 1131 (9th Cir.2007) (coming to the same conclusion).
This case does not come anywhere near to closely resembling the cases in which the Supreme Court has found presumptive bias. In this case, the judge's wife was an acquaintance of the victim of the crime that the defendant was accused of committing. Judge Henry Wade, Jr. did not have a pecuniary interest in the outcome of the case, was not abused or criticized by Richardson, and did not investigate and adjudicate the case. Thus, the Texas court of appeals' decision to overrule Richardson's complaint as well as the Texas Court of Criminal Appeals' decision to deny his application for habeas relief were not contrary to and did not involve an unreasonable application of "clearly established Federal law, as determined by the Supreme Court of the United States" for the purposes of 28 U.S.C. § 2254(d)(1).
Nonetheless, language in some Supreme Court opinions implies that there may be presumptive bias when a trial judge appears to be biased in situations other than those listed above. For example, the Supreme Court has indicated that recusal for the appearance of bias is required by the Due Process Clause when the situation is one "which would offer a possible temptation to the average ... judge to ... lead him not to hold the balance nice, clear and true." Aetna, 106 S.Ct. at 1585 (quoting Ward, 93 S.Ct. at 83); see also Couch, 896 F.2d at 82 ("The Due Process Clause requires a judge to step aside when a reasonable judge would find it necessary to do *476 so."). As the Supreme Court has explained, the Due Process Clause "may sometimes bar trial by judges who have no actual bias and who would do their very best to weigh the scales of justice equally between contending parties." Aetna, 106 S.Ct. at 1587. Furthermore, the Supreme Court has indicated that "to perform its high function in the best way, `justice must satisfy the appearance of justice.'" Id. (citing In re Murchison, 349 U.S. 133, 75 S.Ct. 623, 625, 99 L.Ed. 942 (1955)).
Richardson incorrectly contends that this language from Supreme Court opinions suggests that an appearance of bias in a trial judge always amounts to presumptive bias requiring recusal. As the Seventh Circuit has explained, the Supreme Court's "`appearance of justice' language" indicates that "judges sometimes must recuse themselves when they face possible temptations to be biased, even when they exhibit no actual bias." Del Vecchio v. Illinois Dep't of Corr., 31 F.3d 1363, 1372 (7th Cir.1994) (en banc). However, not all "possible temptations" toward bias require a judge to disqualify himself. Id. at 1374. Judge Henry Wade, Jr. did not face a significant temptation to be biased against Richardson. He did not stand to gain personally or professionally if Richardson were sentenced more harshly by the jury. It may have pleased his wife or her friends and acquaintances at the Junior League if Richardson received a harsh sentence, but this is not the type of "possible temptation" that would lead the average judge "not to hold the balance nice, clear and true." Aetna, 106 S.Ct. at 1585. Thus, this case does not present the situation contemplated by the Supreme Court in which a violation of due process would result when a judge was not actually biased.
More importantly, it is only clearly established by Supreme Court precedent that presumptive bias exists in the three circumstances discussed above. Simply attempting to apply to a particular situation such non-specific highly general dicta as cited by Richardson does not suffice to meet the "clearly established" standard here. See Lockyer, 123 S.Ct. at 1172-73. Thus, even if the appearance of bias may constitute presumptive bias and require reversal in situations other than those outlined by the Supreme Court, the Texas state courts did not improperly deny Richardson relief in violation of clearly established Supreme Court precedent.
Fifth Circuit case law supports our conclusion that there is no "clearly established Federal law" supporting Richardson's argument that the appearance of bias in Judge Henry Wade, Jr. violated his due process rights, and amounted to structural error.[6] For example, in Bradshaw v. McCotter, 785 F.2d 1327, 1329 (5th Cir. 1986) (Bradshaw I), revised by Bradshaw v. McCotter, 796 F.2d 100 (5th Cir.1986) (Bradshaw II), this court held that the presence of an appellate judge's name on the state's brief without more created an appearance of bias requiring automatic vacatur under the Due Process Clause without harmless error analysis. However, on panel rehearing, the court followed the analysis of the recently-released opinion in Aetna and concluded that the constitutional *477 violation required reversal only if the appearance of bias was prejudicial. Bradshaw II, 796 F.2d at 101. Because the appellate judge's vote was not controlling in Bradshaw's case, Bradshaw suffered no prejudice as a result of the judge's appearance of bias. Id. This court held that the judge should have recused, but that his failure to do so did not amount to a due process violation. Id. Thus, Bradshaw II suggests that the appearance of bias in a trial judge does not per se amount to a due process violation or a structural error.
This court came to a similar conclusion in Couch, 896 F.2d 78. In Couch, we analyzed whether an appearance of judicial bias, without a claim of actual bias, warranted a claim for habeas relief under 28 U.S.C. § 2255.[7] 896 F.2d at 80. The petitioner claimed that his trial judge created an appearance of partiality in violation of the Due Process Clause and the federal recusal statute, 28 U.S.C. § 455, because he did not disclose that he invested money in an unsuccessful oil drilling venture with the defendant and that he shared leasehold rights with the defendant's children in an oil and gas lease. Id. at 79. This court emphasized that section 455 establishes a more demanding standard than the Due Process Clause because it involves the "additional, systemic concern for avoiding the appearance of impropriety." Id. at 82. It held that the Due Process Clause did not require vacatur of the defendant's sentence based on the connections between the trial judge and the defendant that may have created the appearance of partiality. Id. Thus, Couch supports the conclusion that the appearance of bias in a judge does not necessarily amount to presumptive bias.
However, Richardson cites one Seventh Circuit case that provides some support for his argument. In Franklin v. McCaughtry, 398 F.3d 955, 960 (7th Cir. 2005), the Seventh Circuit reviewed a Wisconsin state court decision rejecting the defendant's challenge to the partiality of the trial judge because he failed to show actual bias. The state court's recusal test, like the test applied by the Texas appellate court here, included first an objective examination of whether a reasonable person could question the judge's impartiality and, second, an analysis of whether this error was harmless. Id. Citing Bracy v. Schomig, 286 F.3d 406, 410-11 (7th Cir.2002) (en banc), the Seventh Circuit held that the state's test was contrary to clearly established federal law because both actual bias and the appearance of bias in a trial judge violate a defendant's due process rights, and both are considered structural errors subject to automatic reversal. Franklin, 398 F.3d at 960-61. In Bracy, the Seventh Circuit stated in dicta that the pertinent Supreme Court cases "tell us that ordinarily `actual bias' is not required, the appearance of bias is sufficient to disqualify a judge." 286 F.3d at 411. However, this is not necessarily an accurate statement of the law. In 1994, the Seventh Circuit actually held in Del Vecchio that the mere appearance of impropriety in a judge does not necessarily render a judgment in violation of due process. Del Vecchio, 31 F.3d at 1371-72 ("[T]he Supreme Court's mention of `appearance of justice' certainly does not compel reversal on due process grounds if a federal judge decides  based on a personal view of judicial protocol that it looked bad for a state judge to try a case.").
*478 Further, the Franklin court did not rest its holding solely on its conclusion that the appearance of bias in a trial judge violates a defendant's due process rights. Its conclusion that a due process violation had occurred was also (indeed apparently primarily) based on a determination that the judge was actually biased. 398 F.3d at 961, 962 (concluding "in the alternative that the Wisconsin Court of Appeals unreasonably determined that [the judge] was not actually biased," and ultimately holding that "[b]ecause [the judge] was actually biased, [the defendant] is entitled to a new trial"). Thus, Franklin is an unreliable guide in this case because it is factually distinguishable (as actual bias was shown) and in other respects seems in some tension with its own circuit's precedents. Furthermore, it is not binding precedent for this court, and is contrary to the holdings of this circuit as in Couch.
A number of other cases from our sister circuits have held that there is no "clearly established Federal law, as determined by the Supreme Court" for the purposes of 28 U.S.C. § 2254(d)(1) that establishes presumptive bias and requires automatic recusal of a judge under the Due Process Clause in cases of a mere appearance of judicial bias alone. See, e.g., Davis v. Jones, 506 F.3d 1325, 1333 (11th Cir.2007) (holding that "none of the Supreme Court cases relied upon by [the defendant] establishes that an appearance [of judicial bias] violates the Due Process Clause"); Welch v. Sirmons, 451 F.3d 675, 700 (10th Cir. 2006) (holding that Supreme Court case law has not held, or even pronounced in dicta, that the mere appearance of bias in a state trial judge violates the Due Process Clause); Johnson v. Carroll, 369 F.3d 253, 263 (3rd Cir.2004) (holding that "the Supreme Court's case law has not held, not even in dicta, let alone `clearly established,' that the mere appearance of bias on the part of a state trial judge, without more, violates the Due Process Clause"); United States v. Lowe, 106 F.3d 1498, 1504 (10th Cir.1997) ("To state a due process claim that a judge was biased, defendant must show either that actual bias existed, or that an appearance of bias created a conclusive presumption of actual bias."); Del Vecchio, 31 F.3d at 1371-72 (Seventh Circuit holding that the "Supreme Court has never rested the vaunted principle of due process on something as subjective and transitory as appearance"). These cases have recognized that the Supreme Court does not require reversal of a defendant's case on due process grounds merely because a judge may have appeared to be biased.
For the reasons stated above, as to the first issue certified on appeal, we hold that the district court correctly concluded that it was not a federal due process violation or federal constitutional structural error, for the Texas courts to refuse to grant Richardson a new trial based on the appearance of bias in Judge Henry Wade, Jr. There is no clearly established law determined by the Supreme Court indicating that the mere appearance of bias in a trial judge such as to mandate recusal under state law constitutes a violation of the Due Process Clause, and requires automatic reversal in a case like Richardson's. Therefore, the Texas courts' decisions denying Richardson relief on his judicial recusal claim were not "contrary to," and did not involve an "unreasonable application of[ ] clearly established Federal law, as determined by the Supreme Court." 28 U.S.C. § 2254(d)(1).

C. Deference to the Texas Court of Appeals
Richardson asks this court to defer to the Texas appellate court's finding that Judge Henry Wade, Jr. should have been recused under Texas law because *479 "the undisputed evidence" showed that "a reasonable member of the public, knowing all the circumstances involved, would have questions or doubts as to the impartiality of the trial judge." Richardson, 83 S.W.3d at 358-59. He argues that the district court failed to recognize that this "finding" by the state appellate court necessarily included a finding of a due process violation. However, the Texas Court of Appeals in Richardson based its recusal holding entirely on "undisputed facts," it made no finding on any disputed historical facts, and essentially simply made a legal determination, not a fact finding, that on those undisputed facts Texas law mandated recusal.
The Texas Court of Criminal Appeals has stated that bias "may be a ground for disqualification only when it is shown to be of such nature, and to such extent, as to deny the defendant due process of law." Kemp v. State, 846 S.W.2d 289, 305 (Tex. Crim.App.1992) (en banc). Under Kemp, a state court deciding a recusal question based on bias "must decide whether the movant has provided facts sufficient to establish that a reasonable man, knowing all the circumstances involved, would harbor doubts as to the impartiality of the trial judge." Id. However, as we expressly said in Couch, the section 455 recusal standard (similar to the Kemp standard) of "where others would have reasonable cause to question the judge's impartiality" is "more demanding than that imposed by the due process clause" which we described, relying on the Supreme Court's opinion in Aetna, as being "when a reasonable judge would find it necessary to do so." Couch at 82 (emphasis added).
The district court correctly concluded that it need not defer to the state court's decision because the due process standard differs from the recusal standard applied by the Texas appellate court. The state appellate court made the required determination under Kemp. Richardson, 83 S.W.3d at 358-59. However, this does not indicate that the state court also necessarily made a factual finding of a federal due process violation. As noted, the court merely made a determination of the legal consequence of the undisputed facts, not a factual finding. And, it expressly stated there was no finding of actual bias, prejudice or partiality. The Texas court of appeals did not mention the Due Process Clause of the federal constitution in its opinion, and did not apply a federal constitutional standard in determining whether Judge Henry Wade, Jr. should have been recused. As the state court applied a more demanding standard in its recusal holding than this court must apply in determining whether Richardson's federal due process rights were violated by Judge Henry Wade, Jr.'s having presided at the trial, we hold that as to the second issue certified on appeal, the decision of the Texas court of appeals did not necessarily include a factual finding of a federal due process violation, and that this court owes it no deference with respect to the federal due process claim.
Moreover, and in any event, our concern under section 2254(d) is with the actual facts determined by the state court and the "ultimate decision" of the state court, and not with "every jot of [their] reasoning." Santellan, 271 F.3d at 193, 194. We accept all the facts reflected in the Texas Court of Appeals' opinion in Richardson respecting Judge Henry Wade, Jr.'s relationship to, participation in and conduct concerning the case.[8] The only question *480 then becomes, under section 2254(d), whether on those facts the Texas appellate court's decision, that Judge Henry Wade, Jr.'s presiding at the trial (over Richardson's timely objection) did not entitle Richardson to a new trial (where, it found beyond a reasonable doubt, there was no prejudice), constitutes 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." We hold that that decision does not meet that test. The Texas appellate court's implied intermediate steps of legal reasoning are ultimately irrelevant to our said holding.

CONCLUSION
For the foregoing reasons, the judgment of the district court denying Richardson's application for writ of habeas corpus is
AFFIRMED.
NOTES
[1]  With regards to its harmless error analysis, the court of appeals stated,

"[c]onsidering the totality of the record, including the fact that the jury assessed Richardson's punishment; the severity of the crime which he committed; and the lack of any showing that the judge did anything during the punishment hearing indicating bias or partiality, we hold that Richardson's substantive rights were not affected, and we further hold, beyond a reasonable doubt, that any error in denying his motion to recuse did not contribute either to his conviction or punishment. Richardson makes no argument that he was harmed and presents no authority with respect to harm." Richardson, 83 S.W.3d at 360.
Tex.R.App. P. 42.2 provides in relevant part:
"44.2. Reversible Error in Criminal Cases
(a) Constitutional Error. If the appellate record in a criminal case reveals constitutional error that is subject to harmless error review, the court of appeals must reverse a judgment of conviction or punishment unless the court determines beyond a reasonable doubt that the error did not contribute to the conviction or punishment.
(b) Other Errors. Any other error, defect, irregularity, or variance that does not affect substantial rights must be disregarded."
[2]  Despite the fact that the Texas trial and appellate courts as well as the United States district court all found that Judge Henry Wade, Jr. was not actually biased, at several points in his brief, Richardson appears to argue that the judge was actually biased against him. He supports his argument by referring to various evidentiary rulings made by the judge, the fact that the judge raised his bond without notice, and the fact that the judge is connected to the victim through his wife. Richardson made these arguments in his COA application, but this court did not grant a COA on that issue. Because this court granted a COA only on the issue of whether the appearance of bias was a structural error, any claim of actual bias is not properly before the court. See § 28 U.S.C. § 2253(c); Lackey v. Johnson, 116 F.3d 149, 151-52 (5th Cir. 1997) (holding that review of a habeas petition is limited to the issues specified in the COA). Moreover, we think it clear that the evidence does not support, and certainly does not compel, a finding of actual bias.
[3]  The state argues that it is questionable whether Richardson adequately and timely raised federal due process arguments in his state court proceedings. Thus, it contends that Richardson did not exhaust his state court remedies on this issue. However, we need not address this argument because we deny Richardson relief regardless of whether this allegation concerning failure to exhaust is accurate.
[4]  Generally, the constitutional due process requirements regarding judicial impartiality are much narrower than the requirements found in recusal statutes and ethical canons. See, e.g. United States v. Couch, 896 F.2d 78, 81 (5th Cir.1990) (stating that 28 U.S.C. § 455, the federal recusal statute, "establishes a statutory disqualification standard more demanding than that required by the Due Process Clause"). Thus, a violation of a state or federal statute for the failure to recuse a trial judge because certain circumstances may give rise to an appearance of bias on the part of the judge does not necessarily constitute a due process violation. In applying the due process standard for judicial recusal, we do not deny the importance of fostering an appearance of impartiality in the judiciary. See Potashnick v. Port City Construction Co., 609 F.2d 1101, 1111 (5th Cir.1980). This principle is well established in the statutes and ethical canons that govern both state and federal judges. Id. For example, 28 U.S.C. § 455(a) requires recusal in a proceeding where a federal judge's "impartiality might reasonably be questioned." The concern with maintaining the appearance of judicial impartiality "stems from the recognized need for an unimpeachable judicial system in which the public has unwavering confidence." Potashnick, 609 F.2d at 1111. However, in this case our only concern is whether the Texas court of appeals' affirmance of Richardson's conviction and sentence, despite its holding that the trial judge should have been recused, violated Richardson's federal due process rights.
[5]  For example, in Aetna, the Supreme Court held that a state judge's participation in an appellate decision violated due process because the decision increased the legal status and settlement value of a case in which the judge was a party. 106 S.Ct. at 1587; see also Ward v. Vill. of Monroeville, 409 U.S. 57, 93 S.Ct. 80, 83, 34 L.Ed.2d 267 (1972) (mayor disqualified under the Due Process Clause from adjudicating traffic cases because the traffic fines contributed significantly to city finances); Tumey v. Ohio, 273 U.S. 510, 47 S.Ct. 437, 441, 71 L.Ed. 749 (1927) (mayor could not sit as judge in cases because he was paid more for a conviction than for an acquittal). In Mayberry v. Pennsylvania, 400 U.S. 455, 91 S.Ct. 499, 505, 27 L.Ed.2d 532 (1971), the Court held that it violated the Due Process Clause to allow a judge who was verbally attacked by a defendant to preside over the defendant's contempt trial because after he had been slandered by the defendant, he was not likely to be able to remain calm and detached in order to adjudicate fairly. Finally, in In re Murchison, 349 U.S. 133, 75 S.Ct. 623, 627, 99 L.Ed. 942 (1955), the Court held that a judge violated due process by acting both as a one-man grand jury and the presiding jurist at the trial of the same defendant.
[6]  Richardson cites two irrelevant Fifth Circuit cases in support of his argument that the appearance of bias constitutes structural error, Republic of Panama v. American Tobacco Co., 217 F.3d 343 (5th Cir.2000), and United States v. Anderson, 160 F.3d 231 (5th Cir. 1998). Neither of these cases addresses the due process standard for judicial disqualification. They apply the standard for judicial recusal under the federal recusal statute, 28 U.S.C. § 455. Republic of Panama, 217 F.3d at 346; Anderson, 160 F.3d at 233. Thus, these cases have no bearing on this case, and do not support Richardson's arguments.
[7]  Section 2255 allows a federal prisoner to file an application for federal habeas corpus relief. It does not establish the same standard of review set forth in section 2254(d), which applies to state prisoners filing federal habeas applications.
[8]  We view the Texas court of appeals' determination that from the recited "undisputed" facts "a reasonable member of the public, knowing all the circumstances involved, would have questions or doubts as to the impartiality of the trial judge," as being, if not simply a legal conclusion, then at the most being a mixed question of law and fact reviewed de novo under § 2254(d)(1). See Horn, 508 F.3d at 312. The underlying, historic facts recited by the Texas court of appeals are all accepted by us as accurate.
