OPINION
SMITH, Circuit Judge.Johnny Martinez was convicted of second-degree murder and sentenced to thirty-five years’ imprisonment. He subsequently filed a habeas petition under Virgin Islands law, which the Superior Court denied. Martinez now appeals the denial of his habeas petition, contending that due process required his sentencing judge and habeas judge to recuse themselves and that the Virgin Islands sentencing provision for second-degree murder is unconstitutionally vague. Because none of his arguments have merit, we will affirm the denial of his habeas petition.
*186I.
In May 1997, Martinez shot and killed Ean Pemberton outside a Pueblo supermarket on St. Croix in the Virgin Islands.1 The Government of the Virgin Islands charged Martinez with first-degree murder in violation of 14 V.I.Code § 922(a)(1) and unauthorized possession of a firearm during commission of a violent crime in violation of 14 V.I.Code § 2253(a). The case was filed in the Superior Court of the Virgin Islands2 and assigned to Judge Edgar Ross, who subsequently recused himself. As a result, then-Judge Maria M. Cabret (now a justice on the Virgin Islands Supreme Court) was reassigned to Martinez’s case. Her courtroom bailiff, Iris Pemberton, was the victim’s aunt.
Several months later, Martinez entered into a plea agreement with the Government and entered an Alford plea3 to second-degree murder in violation of 14 V.I.Code § 923(b) and unauthorized possession of a firearm. In exchange, the Government recommended consecutive sentences of thirty-five years for second-degree murder and ten years for unauthorized possession of a firearm.
Judge Cabret eventually adopted both of these recommendations, though the thirty-five-year recommendation for second-degree murder took a more circuitous path. On that count, Judge Cabret initially sentenced Martinez to life imprisonment—a sentence that the law did not authorize. See Ruiz v. United States, 365 F.2d 500, 501 (3d Cir.1966) (holding that the Virgin Islands sentencing statute for second-degree murder, by setting a minimum sentence without a maximum sentence, authorizes any sentence for a term of years above the minimum but does not authorize life imprisonment). The Government alerted Judge Cabret to this error, which she fixed by amending Martinez’s life sentence to seventy-five years’ imprisonment. Martinez appealed to the Appellate Division of the United States District Court for the Virgin Islands,4 claiming that his seventyfive-year sentence was unconstitutionally disproportionate to his crime. The Appellate Division affirmed his sentence on November 23, 1999. Back before Judge Cabret in Superior Court, Martinez moved for a reduction of his sentence. In February 2000, Judge Cabret granted that motion, reducing his seventy-five-year sentence to thirty-five years—the Government’s original recommendation.
Martinez was still dissatisfied with his sentence. In January 2003, he petitioned the Superior Court for a writ of habeas corpus under 5 V.I.Code § 1303, and the case was assigned to Judge Cabret, his sentencing judge. Martinez argued that Judge Cabret should have recused herself from presiding over his criminal case, that the Virgin Islands sentencing provision for *187second-degree murder was unconstitutionally vague because it did not set a maximum penalty, and that his sentence violated his right to equal protection because it was harsher than other similarly situated defendants. Later that year, Judge Ca-bret recused herself from Martinez’s habe-as case without explanation, citing 4 V.I.Code §§ 284(4) and 285, which require recusal if there is the appearance of bias. Martinez’s habeas petition was reassigned to Judge Ross—the same judge who had recused himself from Martinez’s criminal case. Judge Ross denied Martinez’s habe-as petition in October 2004 and subsequently denied Martinez’s motion for reconsideration.
Martinez appealed the denial of his ha-beas petition to the Appellate Division under 48 U.S.C. § 1613a(a), beginning a protracted journey up and down the appellate ladder on various procedural issues. On April 26, 2005, the Appellate Division remanded the case to the Superior Court to determine whether a certificate of probable cause should be issued under Virgin Islands Rule of Appellate Procedure 14(b), which requires such a certificate before a habeas petitioner may appeal the denial of his petition. See Mem. Op., Docket Entry (“D.E.”) 39 at 2. But in December 2005, Judge Ross refused to follow Rule 14 on remand (either by granting a certificate of probable cause or explaining why he was denying it). Id. at 3. Judge Ross believed that Rule 14’s certificate requirement was a substantive rule of law that exceeded the Appellate Division’s procedural rulemaking authority. Id.
On January 5, 2007, before the Appellate Division, the Government moved to dismiss Martinez’s appeal before the Appellate Division for lack of jurisdiction because no certificate of probable cause had been issued. Martinez subsequently filed the opening brief in his appeal of the denial of his habeas petition. But in April, Martinez moved to amend his opening brief to add a new argument—that due process required Judge Ross to recuse himself from ruling on Martinez’s habeas petition—and Martinez also filed his opposition to the Government’s motion to dismiss his appeal.
In February 2008, the Appellate Division remanded the case again to the Superior Court to consider whether to issue a certificate of probable cause. See Mem. Op., D.E. 39 at 5. The Appellate Division apparently never ruled on Martinez’s motion to amend his opening brief. While the case was pending before the Superior Court for a certificate of probable cause, Martinez asked the Appellate Division to suspend the probable-cause requirement of Rule 14 because he believed it was unconstitutional for violating the principle of separation of powers. In November 2010, the Appellate Division held that it could retain post-remand jurisdiction over Martinez’s motion and took his motion under advisement.
By January 2011, the Superior Court had still not ruled on whether to grant Martinez a certificate of probable cause so that he could appeal the denial of his habeas petition. So Martinez appealed the dismissal of his case to this Court and also petitioned this Court for a writ of mandamus directing the Appellate Division to exercise post-remand jurisdiction over the denial of his habeas petition. See In re Martinez, 422 Fed.Appx. 92, 93 (3d Cir.2011) (per curiam). After filing his appeal and petition in this Court, the Superior Court finally issued a certificate of probable cause. Id. at 94. Consequently, this Court dismissed Martinez’s appeal for lack of jurisdiction and denied his petition for a writ of mandamus. Id. at 94-95.
With a certificate of probable cause in hand, the Appellate Division proceeded to *188consider Martinez’s appeal of his habeas petition on May 18, 2011. Martinez had already filed his opening brief in January 2007, so the Appellate Division set a briefing schedule for the Government’s response brief and Martinez’s reply brief. The Government, however, never filed its response brief. See Mem. Op., D.E. 104 at 23 n.26. On July 7, 2011, the Appellate Division affirmed the Superior Court’s denial of Martinez’s habeas petition, more than six years after Martinez had first filed his appeal. See id.
Martinez timely appealed the merits of his habeas petition to this Court.5
II.
Martinez says that due process required his sentencing judge, Judge Cabret, to recuse herself from presiding over his criminal case.6 Appellant’s Br. at 28. Although “[a] fair trial in a fair tribunal is a basic requirement of due process,” In re Murchison, 349 U.S. 133, 136, 75 S.Ct. 623, 99 L.Ed. 942 (1955), “most matters relating to judicial disqualification d[o] not rise to a constitutional level,” FTC v. Cement Institute, 333 U.S. 683, 702, 68 S.Ct. 793, 92 L.Ed. 1010 (1948). Due process requires recusal only when a judge “has a direct, personal, substantial, pecuniary interest in a case” or when there are “circumstances in which experience teaches that the [objective] probability of actual bias on the part of the judge or decision-maker is too high to be constitutionally tolerable.” Caperton v. A.T. Massey Coal Co., 556 U.S. 868, 876-77, 129 S.Ct. 2252, 173 L.Ed.2d 1208 (2009) (internal quotation marks and citations omitted). Martinez relies on both grounds: (1) that Judge Cabret’s “harsh” and unauthorized initial sentence of life imprisonment shows that she was actually biased against him, and (2) that Judge Cabret’s friendship and work relationship with her bailiff, the aunt of Martinez’s victim, created a serious risk of actual bias requiring recusal.
Neither argument passes muster. “[J]udicial rulings alone almost never constitute a valid basis” requiring recusal. Mass. Sch. of Law at Andover, Inc. v. Am. Bar Ass’n, 107 F.3d 1026, 1043 (3d Cir.1997) (quoting Liteky v. United States, 510 U.S. 540, 555, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994)). If anything, the record in this case demonstrates that Judge Cabret acted impartially: Although she initially erred by imposing an unauthorized life sentence for second-degree murder, she *189promptly corrected that error by changing Martinez’s life sentence to a seventy-five year sentence. And when Martinez subsequently asked her to reduce that seventy-five year sentence, she did so by cutting it nearly in half. Such evenhanded treatment is hardly the mark of a biased judge.
Nor does Judge Cabret’s relationship with the victim’s aunt present one of the “extraordinary situation[s] where the Constitution requires recusal” because of the serious risk of actual bias. Caperton, 556 U.S. at 887, 129 S.Ct. 2252. Our sister courts of appeals have consistently refused to hold that due process mandates recusal based on nothing more than a judge’s familial or official relationships to others in the courtroom. See, e.g., Clemens v. U.S. Dist. Court for the Cent. Dist. of Cal., 428 F.3d 1175, 1180 (9th Cir.2005) (“Mandatory disqualification ... is not warranted simply because of a professional relationship with a victim.”); Fero v. Kerby, 39 F.3d 1462, 1479 (10th Cir.1994) (holding that due process does not mandate recusal in a criminal case where the judge’s son worked for the prosecution and the judge’s brother-in-law was plaintiffs counsel in a wrongful death action arising out of the criminal case because these interests were “too remote and insubstantial to create a presumption of bias”); Dyas v. Lockhart, 705 F.2d 993, 997 (8th Cir.1983) (holding that there was not an unconstitutionally high probability of actual bias where a defendant was convicted of felony-murder before a judge whose nephew, brother, and son were prosecuting the case and his wife was the court reporter). And as we have previously explained, the Supreme Court has never held “that an appearance of bias on the part of a judge, without more, violated the Due Process Clause.” Johnson v. Carroll, 369 F.3d 253, 262 (3d Cir.2004). To the contrary—the Constitution leaves regulation of such “matters of kinship” and “remoteness of interest” to “legislative discretion.” Caperton, 556 U.S. at 876, 129 S.Ct. 2252 (quoting Tumey v. Ohio, 273 U.S. 510, 523, 47 S.Ct. 437, 71 L.Ed. 749 (1927)). Consequently, due process did not require Judge Cabret to recuse herself.
III.
Martinez similarly argues that due process required Judge Ross to recuse himself from ruling on Martinez’s habeas petition because Judge Ross’s “brother is married to the victim’s wife’s aunt.” Appellant’s Br. at 10. As a threshold matter, Martinez has waived this argument. He did not present this argument in his opening brief before the Appellate Division. Although he later moved to amend his brief to include this argument and the Appellate Division did not explicitly rule on his motion to amend, the Appellate Division impliedly denied his motion by not addressing this argument in its opinion upholding the denial of his habeas petition. Moreover, Martinez did not mention this argument again to the Appellate Division during the more-than-four years that passed between his attempt to amend his brief and the Appellate Division’s ruling, despite the case moving up and down the appellate ladder multiple times during that period. Martinez therefore did not “unequivocally” present this argument to the lower court “in a manner that permitted] the court to consider its merits.” Shell Petroleum, Inc. v. United States, 182 F.3d 212, 218 (3d Cir.1999).
At all events, for the same reasons that Judge Cabret’s working relationship and friendship with the victim’s aunt did not require recusal, Judge Ross’s remote familial relationship with Martinez’s victim did not require him to recuse himself from ruling on Martinez’s habeas petition. See United States v. Mansoori, 304 F.3d 635, *190667 (7th Cir.2002) (“Conflicts arising from the judge’s familial relationships normally do not mandate recusal under the due process clause.” (citing Aetna Life Ins. Co. v. Lavoie, 475 U.S. 813, 820, 106 S.Ct. 1580, 89 L.Ed.2d 823 (1986))).
IV.
Martinez argues that 14 V.I.Code § 923—the Virgin Islands sentencing provision for second-degree murder—is unconstitutionally vague because it sets a five-year minimum penalty without setting a maximum penalty. Appellant’s Br. at 14. Under the Constitution’s Due Process Clause, a sentencing provision is unconstitutionally vague if it fails to give notice that the punishment imposed is one of the possible penalties. Gov’t of the Virgin Islands v. D.W., 3 F.3d 697, 699 (3d Cir.1993) (citing United States v. Batchelder, 442 U.S. 114, 121, 99 S.Ct. 2198, 60 L.Ed.2d 755 (1979)). We review the constitutionality of a federal statute de novo. Abdul-Akbar v. McKelvie, 239 F.3d 307, 311 (3d Cir.2001). ‘Where, as here, a statute does not involve rights guaranteed by the First Amendment, we examine whether it is vague as applied to the affected party.” United States v. Fullmer, 584 F.3d 132, 152 (3d Cir.2009) (internal quotation marks omitted).
Martinez’s void-for-vagueness argument fails. Our sister courts of appeals have repeatedly and uniformly rejected the argument that a criminal statute is unconstitutionally void just because it does not establish a maximum penalty. See, e.g., United States v. Davis, 801 F.2d 754, 756-57 (5th Cir.1986) (“It is well established that sentencing statutes are not unconstitutionally vague for failure to fix a maximum sentence.”), superseded by statute, 18 U.S.C. § 924; United States v. Bridges, 760 F.2d 151, 154 (7th Cir.1985) (rejecting the argument that 18 U.S.C. § 841(b)(1)(A) is unconstitutional because it failed to specify a maximum sentence); United States v. Sims, 529 F.2d 10, 12 (8th Cir.1976) (“Due process is not violated by failure of a sentencing statute to specify the maximum sentence of imprisonment or parole.” (internal quotation marks and citations omitted)); Binkley v. Hunter, 170 F.2d 848, 849-50 (10th Cir.1948) (“Under a statute such as this, fixing a minimum sentence and leaving the imposition of the maximum sentence to the court, and the only limitation upon the power of the court in imposing sentence would be that of the Eighth Amendment....”). And Martinez does not cite any authority to the contrary. Indeed, our prior decisions make clear that § 923 authorizes imprisonment for any “fixed definite term of years” (that is, not life imprisonment), see Ruiz, 365 F.2d at 501, a range that squarely includes Martinez’s thirty-five-year sentence. See United States v. Moyer, 674 F.3d 192, 211 (3d Cir.2012) (“In criminal cases, because vagueness attacks are based on lack of notice, they may be overcome in any specific case where reasonable persons would know their conduct puts [them] at risk of punishment under the statute.” (internal quotation marks and citations omitted)).
Stripped of his void-for-vagueness challenge, Martinez’s real complaint is that his thirty-five-year sentence was unconstitutionally disproportionate to his crime. See Appellant’s Br. at 23 (“If the courts of the Virgin Islands are allowed to continue to arbitrarily and discriminately sentence criminal defendants to lengthy sentences on convictions of second degree murder under 14 V.I.C. § 923(b) without any legally fixed bounds.... ”); id. at 27 (stating that “no one convicted for the same offense in [Martinez’s] sentencing year” received as “harsh” of a sentence as Martinez did). Of course, the Eighth Amendment, “which forbids cruel and unusual punishments,” *191does “contain[] a narrow proportionality principle that applies to noncapital sentences.” United States v. Walker, 473 F.3d 71, 79 (3d Cir.2007) (quoting Ewing v. California, 538 U.S. 11, 20, 123 S.Ct. 1179, 155 L.Ed.2d 108 (2003)). And although this narrow proportionality principle “applies to sentences for terms of years” (such as Martinez’s sentence), “only an extraordinary case will result in a constitutional violation.” Id. (citing Lockyer v. Andrade, 538 U.S. 63, 72, 77, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003)); see also Rummel v. Estelle, 445 U.S. 263, 272, 100 S.Ct. 1133, 63 L.Ed.2d 382 (1980) (“Outside the context of capital punishment, successful challenges to the proportionality of particular sentences have been exceedingly rare.”).
This is not such an extraordinary case. Martinez’s sentence is within the limits set by the Virgin Islands legislature. See United States v. Miknevich, 638 F.3d 178, 186 (3d Cir.2011) (“Generally, a sentence within the limits imposed by statute is neither excessive nor cruel and unusual under the Eighth Amendment. This is so because we accord substantial deference to [the legislature], as it possesses broad authority to determine the types and limits of punishments for crimes.” (citations omitted)). Martinez does not explain why, “as is his burden,” his thirty-five-year sentence for second-degree murder is cruel and unusual. Id. By contrast, the Appellate Division has already sufficiently explained why Martinez’s interim sentence of seventy-five years was not grossly disproportionate to his crime:
Martinez shot the victim from behind and seven more times after he was already down, three of which were to the back of the head. According to the witnesses, Martinez calmly walked around the fallen victim, methodically and repeatedly shooting him. Additionally, the trial court noted the facts before it tending to show that this was a revengeful, purposeful killing.
Virgin Islands v. Martinez, 1999 WL 1273717, at *3, 1999 U.S. Dist. LEXIS 20045, at *10-11 (D.V.I.App.Div.1999). Given the circumstances of his crime and his thirty-five-year sentence, this case does not remotely resemble any of the rare situations in which the difference between the crime and the sentence was unconstitutionally disproportionate. Compare Solem v. Helm, 463 U.S. 277, 281, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983) (holding that the Eighth Amendment prohibited a life sentence without the possibility of parole for a recidivist offender convicted of “uttering a ‘no account’ check for $100”), with Harme-lin v. Michigan, 501 U.S. 957, 961, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991) (rejecting a proportionality challenge to a mandatory sentence of life without the possibility of parole imposed on a first-time offender convicted of possessing 672 grams of cocaine), and Walker, 473 F.3d at 83 (concluding that a defendant’s fifty-five-year sentence for armed robberies and drug-trafficking crimes was not unconstitutional). Consequently, we reject Martinez’s proportionality challenge to his sentence.
V.
Martinez also argues that the Virgin Islands Legislature has unconstitutionally delegated discretion to the Virgin Islands courts to impose any sentence for second-degree murder (above the mandatory minimum of five years). He also argues that this arrangement violates separation of powers. He did not present these arguments in his habeas petition and did not raise these arguments before the District Court. Consequently, these remaining arguments are waived, and we decline to consider them now. Shell Petroleum, Inc., 182 F.3d at 219 (“noting the well-established rule that absent compelling circumstances an appellate court will not consider *192issues that are raised for the first time on appeal” (quoting Patterson v. Cuyler, 729 F.2d 925, 929 (3d Cir.1984))).
Accordingly, we will affirm the denial of Martinez’s habeas petition.
. The parties have not provided any original documentation of the factual and procedural background, but these events do not appear to be in dispute.
. At the time, the Superior Court was known as the Territorial Court of the Virgin Islands. As of January 1, 2005, the name of the Territorial Court changed to the Superior Court. See Act of Oct. 29, 2004, No. 6687, § 1 (2004). For consistency, we refer to this court as the Superior Court throughout this opinion.
. See North Carolina v. Alford, 400 U.S. 25, 38, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970) (holding that, when facing strong evidence of guilt, a defendant may plead guilty while protesting innocence to avoid going to trial).
. At the time, the Virgin Islands had not yet established a local appellate tribunal, and appeals from the Superior Court went to a three-judge panel known as the District Court of the Virgin Islands, Appellate Division. See Gov't of the Virgin Islands v. Hodge, 359 F.3d 312, 316 (3d Cir.2004) (describing the Virgin Islands court system in existence at the time).
. The Appellate Division had jurisdiction over Martinez’s appeal for the same reasons we recently explained in Hughley v. Government of the Virgin Islands, No. 11-3845, 536 Fed.Appx. 278, 283-85, 2013 WL 4492709, *4-6 (3d Cir. Aug. 22, 2013). We have jurisdiction under 48 U.S.C. § 1613a(c) and 28 U.S.C. § 1291. Furthermore, Martinez's appeal to this Court may proceed despite the lack of a certificate of appealability. Under 28 U.S.C. § 2253(c), a defendant in custody pursuant to a sentence of the Superior Court must obtain a certificate of appealability before he can appeal the denial of his habeas petition under 28 U.S.C. § 2254. See Walker v. Gov’t of the Virgin Islands, 230 F.3d 82, 89 (3d Cir.2000). Like habeas petitions under state law, however, the requirements in § 2253 for habeas petitions filed under § 2254 (including the requirement of a certificate of appealability) do not apply to a habeas petition filed under Virgin Islands local law. Martinez’s petition was filed under 5 V.I.Code § 1303 and therefore § 2253's certificate-of-appealability requirement does not apply.
. Before the Appellate Division, Martinez also argued that the Virgin Islands recusal statutes required Judge Cabret’s recusal—-an argument that the Appellate Division rejected on its merits. We do not address this argument because Martinez's briefs in this Court focus on whether due process mandated Judge Ca-bret’s recusal. In any event, we agree with the Appellate Division’s conclusion that the Virgin Islands recusal statutes did not require Judge Cabret’s recusal.