*680David Sanchez, Jr., was serving a term of federal supervised release when he killed someone with a knife. Texas prosecutors dismissed the murder charge, concluding that Sanchez had acted in justifiable self-defense. But Sanchez's conduct still undisputedly violated the condition of supervised release prohibiting him from possessing a deadly weapon. So the district court convened a hearing to assess whether his term of supervised release should be revoked and a revocation sentence imposed. See 18 U.S.C. § 3583(e)(3).
After taking evidence, the district court determined that, contrary to the judgment of Texas prosecutors, Sanchez had not acted justifiably. Specifically, the district court found that Sanchez had unreasonably failed to de-escalate the situation in the lead-up to the homicide. The district court thus determined that an above-Guidelines revocation sentence of 32 months' imprisonment was necessary to protect the public and deter Sanchez's future criminal conduct.
Sanchez appeals that revocation sentence on two grounds. First, he says, the district court improperly based the sentence on the retributive need to punish his post-conviction conduct, which the revocation statute tells us is off limits. See 18 U.S.C. § 3583(e) ; United States v. Miller , 634 F.3d 841, 844 (5th Cir. 2011). And even if the district court did not consider impermissibly retributive factors, Sanchez says, his sentence is still plainly substantively unreasonable because no balancing of the properly-considered factors could justify a term of imprisonment nearly three times as high as the top of the advisory range calculated from the U.S. Sentencing Guidelines Manual. For the reasons explained below, we reject both arguments and affirm.
I
Federal sentences that include a term of imprisonment may sometimes append a term of supervised release, during which time the defendant is let out of prison subject to certain enumerated conditions. See 18 U.S.C. § 3583(a), (d). If the defendant then violates one or more of those conditions, the district court may revoke the term of supervised release and impose a new term of imprisonment, called a "revocation sentence." See id. § 3583(e)(3). That is what happened to Sanchez.
Sanchez had been on supervised release for 14 months when he committed homicide. He received a call one night from his recent ex-girlfriend. She told him that a third person, Jose Hernandez, "wanted to fight him one-on-one." Sanchez later told police that he responded: "You know what, fuck you, come over here. We will fight one-on-one and get it over with." Twenty minutes later, Hernandez arrived at Sanchez's apartment with a group of between five and ten other people. Anticipating a fight, Sanchez grabbed a knife and met them outside. Sanchez stabbed Hernandez. Hernandez died from his wound. A Texas grand jury initially charged Sanchez with murder, but prosecutors dismissed the case ten months later on the ground that Sanchez "had used justifiable deadly force pursuant to Texas Penal Code [sections] 9.31 [and] 9.32."
*681At that point, probation officers informed the federal district court (who had imposed the term of supervised release) that Sanchez had violated his conditions of supervised release by "possess[ing] a dangerous weapon." The probation officers further alleged that Sanchez had violated more of his supervised-release conditions by testing positive for cocaine, but those drug-use allegations played no apparent role in the revocation hearing that followed.
Sanchez pleaded true to all charges at the revocation hearing's outset. Nonetheless, the district court proceeded to inquire extensively into whether Sanchez had reasonably feared for his life, and, in particular, whether he could have done more to extricate himself from the situation. Some of the district court's questions and comments included:
• "He's on supervised release. He gets a call that his girlfriend says somebody is going to come over to do him harm. He does not call the police. He gets a knife and he goes out and kills somebody is the bottom line."
• "He's on my supervised release.... And he didn't call the police before he put a knife in his pocket and went out to fight somebody with a knife."
• "Is there any dispute that [Sanchez] said [in response to the phone call from his ex-girlfriend], 'You know where I live'?"
• "In front of the whole mob [Sanchez] does this [read: attacks Hernandez]? ... He couldn't have been too scared of the mob."
• "Did anybody else have any weapons of any kind? ... And did [Sanchez] have any reason to think that anybody was bringing any kind of deadly force against him? ... Who testified that [Sanchez] was being assaulted? ... Did [Sanchez] have any marks on him at all?"
• "He arms himself with a deadly weapon. There was no indication anybody else had a deadly weapon of any kind."
The district court also repeatedly emphasized the fact that Hernandez had died, referring to him as "the dead person" who had been "slashed open" and whom Sanchez had "stabbed and killed."
When defense counsel objected that the district court was improperly forcing Sanchez to re-litigate the dismissed murder case-which Texas authorities had already deemed a nonstarter-the following exchange occurred:
MR. MORALES: I think we should play all of [the videos]. If we're going to try this as a murder case, then we should play all of them, and that's-
THE COURT: This is a preponderance of the evidence, Mr. Morales.
MR. MORALES: Yes, Your Honor.
THE COURT: I'm not here for beyond a reasonable doubt.
MR. MORALES: Your Honor, but that's not-
THE COURT: This is preponderance of the evidence.
Defense counsel later reframed his objection, contending that the district court could not drive up Sanchez's sentence "because of the outcome" that had resulted from the supervised-release violation-namely, the stabbing death of Hernandez. In response, the district court stated: "I have the authority to go as high as I want to.... I have the powers I feel necessary to protect the public."
The district court then turned to the sentencing factors enumerated in 18 U.S.C. § 3553(a). In doing so, it expressly declined to consider Sanchez's criminal history. The district court instead focused on the needs "to afford adequate deterrence to criminal conduct" and "to protect the public from further crimes."
*682§ 3553(a)(2)(B), (C). The district court's sentencing colloquy provided:
I've looked at the factors of 3553(a), except for his history, I'm not sure it's relevant, but of course, he ... pleaded true to carrying a dangerous weapon, possessing a dangerous weapon. And he's just ... demonstrated what can happen when you do that, and our man is dead by his dangerous weapon.
And I'm looking at deterring future criminal conduct, protecting the public-also I notice from the video that you had me watch-and I'm glad I did-at least it was 20 minutes ... from the time you got the call to the time the people came to the apartment, and there at no time was a phone call made to the police or did he attempt to put himself out of harm's way, if he was in harm's way; no indication that anybody was armed but him and no testimony that anybody laid a hand on him.
Defense counsel recommended a sentence within the advisory range calculated from the policy statements in the U.S. Sentencing Guidelines Manual: 5 to 11 months' imprisonment. The Government made no recommendation. The district court imposed a prison sentence of 32 months. Sanchez appealed.
II
Because we assume without deciding that Sanchez adequately preserved his objections, see Fed. R. Crim. P. 51(b), we follow the law of our circuit and review his revocation sentence under the "plainly unreasonable" standard, United States v. Warren , 720 F.3d 321, 326 (5th Cir. 2013). That standard has two steps. Id. First we evaluate the reasonableness of the sentence using the standards of appellate review applicable to criminal sentences generally. See Gall v. United States , 552 U.S. 38, 46, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). That is, we ask whether the district court committed "significant procedural error, such as failing to consider the [applicable] factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence," United States v. Winding , 817 F.3d 910, 913 (5th Cir. 2016) (quoting Warren , 720 F.3d at 326 ), and we assess "the substantive reasonableness of the sentence imposed under an abuse-of-discretion standard," id. (quoting Miller , 634 F.3d at 843 ). At the second step, however, we vacate the sentence only if the identified error is "obvious under existing law," such that the sentence is not just unreasonable but plainly unreasonable. Miller , 634 F.3d at 843. Law from the "obviousness" prong of Rule 52(b)'s plain error test informs this latter inquiry, see id. at 843-44, notwithstanding that the error was in fact preserved.1
*683A
Sanchez argues primarily that the district court fashioned his revocation sentence based on a perceived need for retribution, which Congress and our caselaw plainly disallow. See 18 U.S.C. §§ 3553(a)(2)(A), 3583(e) ; United States v. Rivera , 784 F.3d 1012, 1016-17 (5th Cir. 2015) ; Miller , 634 F.3d at 844. Although Sanchez characterizes this putative error alternatively as one of both procedure and substance, nothing in our analysis turns on that distinction. See Rivera , 784 F.3d at 1016-17 (not distinguishing between procedural and substantive errors); Miller , 634 F.3d at 844 (same).
General sentencing considerations are set forth in 18 U.S.C. § 3553(a). Among other things, that statute enjoins district courts to "impose a sentence sufficient, but not greater than necessary, to comply with the purposes" enumerated in § 3553(a)(2), namely:
the need for the sentence imposed-
(A) to reflect the seriousness of the offense, to promote respect for the law, and to provide just punishment for the offense;
(B) to afford adequate deterrence to criminal conduct;
(C) to protect the public from further crimes of the defendant; and
(D) to provide the defendant with needed educational or vocational training, medical care, or other correctional treatment in the most effective manner....
§ 3553(a)(2). "These four considerations-retribution, deterrence, incapacitation, and rehabilitation-are the four purposes of sentencing generally, and a court must fashion a sentence 'to achieve the[se] purposes ... to the extent that they are applicable' in a given case." Tapia v. United States , 564 U.S. 319, 325, 131 S.Ct. 2382, 180 L.Ed.2d 357 (2011) (alterations in original) (quoting 18 U.S.C. § 3551(a) ).
But retribution is off the table when it comes to revocation. Revocation sentences are governed by a separate statute, 18 U.S.C. § 3583(e)(3). That statute authorizes district courts to respond to a violation of the conditions of supervised release by imposing a new term of imprisonment, but only "after considering" a list of factors that incorporates most-but not all-of § 3553(a).2 Notably absent from the list are the retributive purposes described in § 3553(a)(2)(A). And "because Congress deliberately omitted" those purposes from the revocation statute, we have held that district courts "may not consider" them in crafting revocation sentences. Miller , 634 F.3d at 844 ; accord Rivera , 784 F.3d at 1016-17. Thus, although district courts are free to consider the aims of deterrence and incapacitation, they may not base their revocation sentences on any perceived need:
• "to reflect the seriousness of the [supervised-release violation3 ]";
*684• "to promote respect for the law"; or
• "to provide just punishment for the [supervised-release violation]."
§ 3553(a)(2)(A) ; see also § 3583(e) ; Rivera , 784 F.3d at 1016-17 ; Miller , 634 F.3d at 844.4 In other words, under our established law, revocation sentences "may not take account of retribution." Tapia , 564 U.S. at 326, 131 S.Ct. 2382.5
Here, however, we are unpersuaded that the district court's sentence took account of retribution. Our reason for thinking so is straightforward: that is not what the district court said it was doing. To the contrary, a plain reading of the transcript shows that the district court (1) found as a factual matter that Sanchez recklessly failed to take available, reasonable steps to remove himself from a situation in which he intended to use a deadly weapon; (2) based on that factual finding, implicitly found that Sanchez posed a potential future criminal threat to the public; and (3) explicitly varied Sanchez's sentence upward to account for the two permissible purposes of revocation sentences: deterring criminal conduct and protecting the public. See § 3553(a)(2)(B), (C). (Whether those purposes adequately justify the sentence on the facts of this case is a separate matter we discuss below.)
This case also differs from the two others in which we have found an improper focus on retribution, in that the district court here never stated that it was basing its sentence on retributive factors. In United States v. Miller , by contrast, the district court quoted § 3553(a)(2)(A) and explained that it was varying upward due to the defendant's "lack of 'respect for the law.' " 634 F.3d at 844. And although the district court in United States v. Rivera was not quite so explicit, we still had no trouble inferring a dominant retributive focus where the district court justified its revocation sentence by stating, "I just don't know that it gets any worse than [what the defendant did]," and by repeatedly characterizing the defendant's conduct as "horrific," "[e]xtremely violent," and "the most serious allegation [of its kind that] I've ever considered." 784 F.3d at 1017. But here, the district court never justified Sanchez's sentence in terms of retributive-sounding concepts like "seriousness," "respect for the law," "justice," or "desert." Instead, the district court explained that it had found Sanchez's conduct so reckless-and so dangerous-that an upward variance was necessary to deter similarly reckless future criminal conduct and, especially, to protect the public.
In response, Sanchez posits that the district court must have harbored a retributive purpose because its entire focus at the revocation hearing was "re-litigat[ing] the dismissed murder case" so it could "ma[k]e its own determination" whether Sanchez *685acted justifiably. Appellant Br. 24-26. Sanchez's basic premise is difficult to dispute: there is no doubt that the district court used the hearing to evaluate Sanchez's conduct in the manner he suggests. But it does not follow, as Sanchez asserts, that the only purpose this inquiry could have served was to gauge the seriousness of Sanchez's conduct and the consonant need to punish him, id. at 26, such that the district court's judgment was "necessarily" retributive, id. at 28. Plainly, whether Sanchez's use of deadly force was justified also bears on his propensity to commit future crimes and/or threaten public safety (as we discuss below).6 Those are permissible purposes of a revocation sentence. And those are the only purposes the district court actually invoked. Even if the district court's inquiry could theoretically have been relevant to an impermissible retributive purpose, we will not assume that the district court in fact had such a purpose in mind-at least where the only purposes the district court actually mentioned were permissible ones. In short, without something in the record to plausibly suggest that the district court based its sentence on the need for retribution (as opposed to deterrence or incapacitation), Sanchez's arguments are unavailing.
B
In the alternative, Sanchez argues that, even if the district court did not err by taking account of retribution, the sentence was still plainly substantively unreasonable. Specifically, he contends (1) that the needs for deterrence and incapacitation, though relevant, cannot justify a sentence almost three times the top of the Guidelines' advisory range; and (2) that the district court abused its discretion by affording no weight whatsoever to Texas's considered decision not to prosecute Sanchez for the same underlying conduct.
We review the substance of a sentencing decision for abuse of discretion. Gall , 552 U.S. at 51, 128 S.Ct. 586. This mode of review "is 'highly deferential,' because the sentencing court is in a better position to find facts and judge their import under the [proper] factors with respect to a particular defendant." United States v. Fraga , 704 F.3d 432, 439 (5th Cir. 2013) (quoting United States v. Hernandez , 633 F.3d 370, 375 (5th Cir. 2011) ). Where, as here, the sentence exceeds the Guidelines' recommendation, we "may consider the extent of the deviation, but must give due deference to the district court's decision that the [relevant] factors, on a whole, justify the extent of the variance." Gall , 552 U.S. at 51, 128 S.Ct. 586. That we might reasonably have concluded that a different sentence was appropriate is insufficient to warrant setting aside the sentence. Id. Rather, we may vacate the sentence only if it "does not account for a factor that should have received significant weight," "gives significant weight to an irrelevant or improper factor," or "represents a clear error of judgment in balancing the sentencing factors." Warren , 720 F.3d at 332. And because the sentence now under review is a revocation sentence, any abuse of discretion must also be "obvious under existing law." Miller , 634 F.3d at 843 ; see supra Part II & note 1. This is a heavy burden for any defendant, made only more difficult here by Sanchez's decision to devote only a single paragraph to the subject.7
*686As to Sanchez's first line of argument, which challenges the district court's reliance on the needs for deterrence and incapacitation, see § 3553(a)(2)(B), (C), we discern no abuse of discretion. The district court made factual findings-uncontested on appeal-that Sanchez violated his conditions of supervised release by engaging in reckless, dangerous conduct. When Sanchez received a call from Hernandez threatening to fight him "one-on-one," Sanchez reacted not by calling the police or taking other steps to avoid the fight, but by accepting the challenge and inviting Hernandez to come over. The district court found that by the time Hernandez arrived, Sanchez still had not called the police. Instead, he had taken a knife from his apartment with the specific intent of attacking Hernandez. The district court also found that there was no reason to believe that anyone else at the scene had a deadly weapon, rendering Sanchez's use of the knife disproportionate and unnecessary. Because the district court found that Sanchez did all this despite the condition of his supervised release expressly forbidding such conduct, the district court reasonably concluded that an above-Guidelines revocation sentence was necessary to accomplish what the term of supervised release had not: that is, deter Sanchez from similarly dangerous and potentially illegal conduct in the future. See § 3553(a)(2)(B). And because Sanchez's conduct undeniably created a significant risk of harm to the public (including to the member of the public whom Sanchez in fact killed), the district court was well-within its discretion to conclude that an above-Guidelines revocation sentence was necessary for the public's protection. See § 3553(a)(2)(C).
Sanchez counters that his knife-possession was not itself "criminal conduct" or a "crime[ ]" within the meaning of § 3553(a)(2)(B) or (C), but that is not necessarily the case. Texas criminalizes intentional homicide. Tex. Penal Code § 19.02. And although a potential defense exists if, among other things, "the actor reasonably believe[d] the force [wa]s immediately necessary to protect the actor against [another person's] use or attempted use of unlawful force," id. §§ 9.31(a), 9.32(a), the district court found "by a preponderance of the evidence" that Sanchez did not reasonably believe that those conditions were met. Sanchez also asserts that the stabbing was "not ... an unprovoked act of violence," but that fact is of no moment. The salient feature is that the stabbing was an avoidable act of violence, justifying the district court's reliance on the goals of deterrence and incapacitation.
As to Sanchez's second line of argument, which faults the district court for not addressing the Texas murder-charge dismissal, we see no obvious error. We find no case supporting Sanchez's position, nor does Sanchez offer one. (Indeed, this portion of Sanchez's argument features no authority at all. See supra note 7.) This is not to say, however, that the dismissal was *687unimportant. More than any federal court, Texas prosecutors are responsible for making Texas-law determinations as to what conduct and which individuals pose criminal threats to public safety. But because an error cannot be "obvious" without authority to support it, United States v. Evans , 587 F.3d 667, 671 (5th Cir. 2009), this is not the type of argument that can prevail under the "plainly unreasonable" test, see Miller , 634 F.3d at 844.8
III
Sanchez's revocation sentence is AFFIRMED.