concurring.
I join much of the majority’s well-reasoned opinion; including its ultimate deci*1118sion to affirm the district court’s dismissal of the Estate’s complaint. See Maj. Op. 1103. I write separately, however, because I question the accuracy of—or at the very least, the necessity of reaching—some of the majority’s interim conclusions.
At the outset, I note that the majority commits to narrowly resolving the many qualified-immunity issues presented in this appeal by focusing, as the district court did, solely on the Estate’s failure to show that defendants violated clearly established law. See Maj. Op. 1107 (expressly “declining] ... to decide each of the constitutional-violation questions first”); Maj. Op. 1110 (noting agreement with, and affir-mance of, district court’s dismissal based on failure to show defendants violated clearly established law). But as I read the majority opinion, it repeatedly, and in my view, unnecessarily, decides the constitutional questions. See, e.g. Maj. Op. 1110 (“Lockett’s suffering did not run afoul of the Eighth Amendment.”); Maj. Op. 1111-12 (suggesting repeated' needle sticks would not violate Eighth Amendmént); Maj. Op. 1114 (“Thus, we conclude that Oklahoma’s use of midazolam comports with the Eighth Amendment.”).
As more fully discussed below, while I agree with the majority’s professed intent to resolve the qualified immunity issues on the clearly-established prong* I do not agree with those portions of the opinion that conflict with that professed intent.
1. Defendants’ Use of Midazolam
First, I respectfully part ways with my colleagues in evaluating whether defendants violated Lockett’s constitutional rights by using a “[n]ew [d]rug [combination.” Maj. Op. 1114 (addressing App. vol. 1, 163-165). In resolving what remains of this claim,1 the majority affirmatively holds that “Oklahoma’s use of midazolam comports with the Eighth Amendment.” Maj, Op. 1114. But I see no reason to reach this constitutional question. As I read its opening brief, the Estate has abandoned its general midazolam claim.
The Estate did allege below that defendants’ general use of midazolam violated Lockett’s Eighth Amendment rights. In support, the Estate asserted that midazo-lam is “incapable of producing a state of unawareness” and that “it cannot relieve pain.”2 App. vol. 1,164. But on appeal, the Estate has pursued a much narrower *1119course. Rather than arguing that defendants violated Lockett’s Eighth Amendment rights by using midazolam generally, the Estate argues only that defendants violated Lockett’s Eighth Amendment rights by using an insufficient dosage of midazolam. See Aplt. Br. 25. ■
It appears that the Estate strategically shifted its argument in an effort to distinguish this case from Warner v. Gross, 776 F.3d 721, 726, 736 (10th Cir.) (affirming district court’s denial of preliminary injunction and denying plaintiffs’ emergency motion for stay of execution despite Oklahoma’s proposed use of midazolam as execution drug), ajfd sub nom. Glossip v. Gross, — U.S.-, 135 S.Ct. 2726, 192 L.Ed.2d 761 (2015). In affirming this court’s decision in Warner, the Supreme Court distinguished between Oklahoma’s current execution protocol (which calls for 500 milligrams of midazolam) and the execution protocol in place when Oklahoma executed Lockett (which instead “called for the administration of 100 milligrams of midazolam”). See Glossip, 135 S.Ct. at 2734. Thus, the Estate argues on appeal, the district court erred in relying on our opinion in Warner “to justify its dismissal of [the Estate’s] claim pertaining to ... use of an insufficient level of’ midazolam, as opposed to the use of midazolam generally. Aplt. Br. 26.
• Whatever the Estate’s motive for making this strategic switch, the result is clear: the Estate has abandoned its claim that defendants violated Lockett’s Eighth Amendment rights by using midazolam in favor of an argument that defendants violated Lockett’s Eighth Amendment rights by using an • insufficient amount of mi-dazolam. Accordingly, I would find the former argument waived and, unlike the majority, I would decline to address it.3
Moreover, I would decline to address the Estate’s current formulation of this argument—i.e., that defendants violated Lockett’s Eighth Amendment rights by using an insufficient dosage of midazolam— because the Estate didn’t advance that argument below. Instead, the complaint asserts that midazolam is inherently incapable of “producing a state of unawareness” or' of “relieving] pain.” App, vol. 1, 164 (“One of the characteristics of midazolam is that it cannot relieve pain.”). But the *1120complaint never suggests that midazolam’s ability to produce unawareness or relieve pain varies depending on the dosage administered.
In fact, to the extent the complaint discusses the constitutional import of the dosage that defendants used in Lockett’s execution at all, it suggests that the dosage was unconstitutionally high, not unconstitutionally low. See, e.g., id. at 165 (“As used in the procedure the high dosage of midazolam carries a substantial risk of producing tonic-clonic seizures and convulsions.”); (“There is a substantial risk of a paradoxical reaction when midazolam is administered in high doses to individuals with a history of aggression or impulsivity.”).
Because the complaint neither explicitly asserts that the defendants violated Lock-ett’s constitutional rights by administering an insufficient dosage of midazolam, nor contains factual allegations that would support such a claim, I would decline to consider whether defendants’ failure to use a higher dosage of midazolam violated Lock-ett’s Eighth Amendment rights. Accordingly, I do not join the portion of the majority opinion addressing the Estate’s midazolam claim.
2. Torture
Likewise, I decline to join the portion of the majority opinion evaluating Lockett’s torture claim. See Maj. Op. 1108-11 (discussing App. vol. 1,161-63). “[I]t is safe to affirm that punishments of torture” violate the Eighth Amendment. Baze, 553 U.S. at 48, 128 S.Ct. 1520 (citation and internal quotation marks omitted). But the question here isn’t whether, “as a broad general proposition,” torture violates the Eighth Amendment. Mullenix v. Luna, — U.S. -, 136 S.Ct. 305, 308, 193 L.Ed.2d 255 (2015) (citation and internal quotation marks omitted). Rather, “[t]he dispositive question is ‘whether the violative nature of [the defendants’] particular conduct is clearly established.’ ” Id. (citation omitted).
The Estate makes no effort to identify any “existing precedent” that might place the question of whether defendants’ “particular conduct” in this case violated the Eighth Amendment’s ban on torture “beyond debate.” Id. (citation and internal quotation marks omitted). Instead, the Estate relies solely on “broad general proposition[s].” Id. (citation and internal quotation marks omitted). For instance, the Estate notes that the Eighth Amendment proscribes “torture[ ] and other barbarous) methods of punishment” and “the unnecessary and wanton infliction of pain,” Estelle v. Gamble, 429 U.S. 97, 102, 103, 97 S.Ct. 285, 50 L.Ed.2d 251 (1976) (citations and internal quotation marks omitted), and that “[p]unishments are cruel when they involve torture or a lingering death.” In re Kemmler, 136 U.S. 436, 447, 10 S.Ct. 930, 34 L.Ed. 519 (1890). See Aplt. Br. 15-17.
While it’s true that there need not be a “case directly on point,” the Supreme Court has repeatedly warned us “not to define clearly established law at a high level of generality.” Mullenix, 136 S.Ct. at 308 (citation and internal quotation marks omitted).4 And that is precisely what the Estate’s citations to Estelle and Kemmler invite us to do here. Because the Estate cites no authority that would have put defendants on notice that their particular *1121conduct violated the Eighth Amendment’s prohibition on torture, the Estate fails to satisfy the clearly-established prong of the qualified-immunity analysis. Accordingly, I would affirm the district court’s conclusion that defendants are entitled to qualified immunity on the Estate’s torture claim on that basis alone, without addressing whether defendants .violated Lockett’s Eighth Amendment right to be free from torture. I therefore do not join the portion of the majority opinion addressing the Estate’s torture claim.
3. Deliberate Indifference
Similarly, while I agree with the majority that the language of the Estate’s “torture” claim is broad enough to alternatively allege that defendants were deliberately indifferent to a risk of substantial harm, I would again find it unnecessary to resolve whether the Estate’s allegations are sufficient to establish that defendants violated Lockett’s constitutional rights. See Maj. Op. 1113-14 (addressing App. vol. 1, Idles).
In its opening brief, the Estate relies primarily on its allegations of repeated needle sticks to support this alternative theory. Aplt. Br. 18-20. But like the majority,- I would decline to consider these allegations because (1) they don’t appear in the complaint and (2) they are not subject to judicial notice. See Maj. Op. 1110-11.
The only remaining factual allegation the Estate relies on in advancing this claim on appeal is its assertion that defendants obscured the injection site with a towel. Aplt. Br. 18. But even assuming that Lock-ett had a constitutional right to have defendants monitor the injection site for the duration of his execution, that right wasn’t clearly established at the time. See Henderson, 813 F.3d at 953 (noting that while a case on point isn’t required, existing precedent must place constitutional question beyond debate). Accordingly, I would affirm solely on that basis, without addressing whether defendants were deliberately indifferent to a “substantial risk of serious harm” in failing to monitor the injection site. See Baze, 553 U.S. at 50, 128 S.Ct. 1520 (citation and internal quotation marks omitted).5
Moreover, even if I reached the constitutional question, I would confine my analy*1122sis to the factual allegations that are properly before us. Because I agree that we shouldn’t take judicial notice of facts that don’t appear in the complaint, I would— unlike the majority—decline to speculate as to whether those same facts might establish an Eighth Amendment violation. Compare Maj. Op. 1110-11 (declining to take judicial notice of Estate’s allegation that defendants “repeatedly stab[bed]” Lockett with a needle), with Maj. Op. 1111 (nevertheless opining, “[W]e doubt that attempting to place an IV for an hour would violate the Eighth Amendment under Baze").
Finally, even if I were to consider whether repeated needle sticks amount to a constitutional violation, I question whether Baze would necessarily resolve the matter, as the majority suggests. See Maj. Op. 1111 (describing Baze as “finding no violation where the execution protocol allowed the IV team one hour to establish an IV”). In Baze, the plurality rejected the petitioners’ assertion that that using an IV inserted after “more than ten or fifteen minutes of unsuccessful attempts is dangerous because the IV is almost certain to be unreliable.” 553 U.S. at 55, 128 S.Ct. 1520 (plurality opinion) (citation and internal quotation marks omitted). The Baze plurality didn’t address whether—as the Estate alleges here, see Aplt. Br. 17-20— repeated needle sticks in and of themselves might at some point raise constitutional concerns.
4. Oklahoma’s Revised Execution Protocol
As a final matter, I am puzzled by the majority's repeated references to Oklahoma’s recent efforts to revise its execution protocol. See, e.g., Maj. Op. at 1113, 1113 n.ll (noting that “[bjecause Oklahoma has changed its execution protocol,” this court will likely “never confront another Oklahoma execution presenting the same circumstances”); Maj. Op. 1115 (“And it’s worth noting that' Oklahoma has now adopted some [new] procedural measures.”).
The question before us on appeal is whether defendants violated Lockett’s clearly established constitutional rights. And Oklahoma’s recent remedial efforts cannot retroactively influence, the constitutional character of defendants’ past actions. Accordingly, Oklahoma’s efforts to revise its execution protocol have played no role in my analysis of the legal issues in this case.
. As the majority correctly notes, the Estate’s opening brief also alleges that defendants violated Lockett’s Eighth Amendment rights by using compounded drugs. Aplt. Br. 24-26. But as the majority points out, the Estate has since withdrawn that allegation in light of defendants' statement that "no compounded drugs were used in Lockett’s execution,” Maj. Op, 1103 n.l.
. The majority declines to accept these allegations as true, and therefore doesn’t address them in analyzing this claim. Maj. Op. 1105 n,5, 1113-15. Again, while I wouldn't reach this abandoned claim, if I were to analyze it I would find the majority’s analysis flawed and I would accept these allegations as true. According to the majority, "[ajsserting that mi-dazolam is ineffective in rendering an inmate unconscious essentially asserts that the use of midazolam is constitutionally deficient, a legal conclusion that we need not credit.” Id. at 1105 n.5. I respectfully disagree. To be sure, the Estate’s factual allegations about midazo-lam’s efficacy may have legal implications— as all relevant factual allegations in a complaint surely must. But that doesn’t necessarily make them legal conclusions. And nothing in Zink v. Lombardi, 783 F.3d 1089 (8th Cir.), cert. denied, — U.S. ——, 135 S.Ct. 2941, 192 L.Ed.2d 976 (2015), indicates otherwise. Contrary to the majority’s suggestion, see Maj. Op. 1105 n.5, the Zink court didn't refuse to accept as true plaintiffs' factual allegations about the potential risks of using compounded pentobarbital. See 783 F.3d at 1099-1103. It simply found those potential risks too hypothetical to demonstrate that the drug was “ 'sure or very likely’ to cause serious-harm or severe pain.” Id. at 1101 (citation omitted).
. Even if defendants’ general-use-of-midazo-lam claim is properly before us, I question the majority's emphasis, in resolving that claim, on the Estate’s failure to allege that defendants chose to use midazolam in order to inflict pain. See Maj. Op. 1114 (“Oklahoma did not switch to midazolam in an effort to inflict additional pain. Thus, we conclude that Oklahoma’s use of midazolam comports with the Eighth Amendment.’’ (citing Baze v. Rees, 553 U.S. 35, 103, 128 S.Ct. 1520, 170 L.Ed.2d 420 (2008) (Thomas, J., concurring))).
That intent to cause pain is an element of any successful method-of-execution claim was, of course, the view of two concurring Justices in Baze. See 553 U.S. at 94, 128 S.Ct. 1520 (Thomas, J., concurring) ("A method of execution violates the Eighth Amendment only if it is deliberately designed to inflict pain.”). But the controlling, plurality opinion in Baze indicates that something less than the intentional infliction of pain may suffice, at least in the context of a pre-execution Eighth Amendment claim: a showing that a prison official is aware that the chosen execution method poses a "substantial risk of serious harm,” but nevertheless adopts'that method in the face of a known-and feasible alternative that will significantly reduce that risk. Id. at 52, 128 S.Ct. 1520 (plurality opinion) (citation and internal quotation marks omitted). See Glossip, 135 S.Ct. at 2738 n.2 (explaining that "THE CHIEF JUSTICE’S opinion in Baze sets out the holding of the case,” while only "Justices SCALIA and THOMAS took the broader position that a method of execution is consistent with the Eighth Amendment unless it is deliberately designed to inflict pain”). Accordingly, I question whether the Estate's, failure to allege that defendants chose midazolam in order to cause Lockett's suffering is dispositive of this claim.
. Mullenix is a Fourth Amendment case, and the Court has explained that "specificity is especially important in [that] context.” 136 S.Ct. at 308. Nevertheless, this court has-applied the same specificity requirement in the Eighth Amendment context. See, e.g., Cox v. Glanz, 800 F.3d 1231, 1245 n.6 (10th Cir. 2015); Henderson v. Glanz, 813 F.3d 938, 953 (10th Cir.2015).
. The majority acknowledges that the Estate's first claim for relief is sufficient to allege deliberate indifference under Baze. See Rule 28(j) Letter, 1 (arguing that complaint asserts deliberate-indifference claim under .Baze)', Maj. Op. 1109 (acknowledging letter, and agreeing that complaint alleges deliberate-indifference claim). Yet—at least as far as I can tell—the majority neither discusses nor applies the Baze plurality's test for deliberate indifference in evaluating this claim. Instead, the majority opinion appears to suggest that because defendants didn’t "place[] the IV or cover[ ] Lockett’s groin area to cause Lockett pain,” the Estate "has no claim for ... deliberate indifference.” Maj. Op. 1110. But as discussed above, see supra note 3, intent to inflict pain is not an element of a deliberate-indifference claim under Baze. Compare Baze, 553 U.S. at 94, 128 S.Ct. 1520 (Thomas, J., concurring), with Baze, 553 U.S. at 49-52, 128 S.Ct. 1520 (plurality opinion). This conclusion likewise calls into question the majority's treatment of the Estate's "[pjrolonged ■ [ejxecution” claim. See Maj. Op. 1113 (indicating that Supreme Court precedent "require[s] that executing officials mean to choose an execution method that will cause extra pain”); Maj. Op. 1113 (citing Baze plurality’s substantial-risk language, but nevertheless focusing on fact that "IV infiltration was ... not something designed to cause additional pain”). Relatedly, I question the majority’s suggestion that defendants weren't deliberately indifferent to Lockett’s serious medical needs simply because they didn’t “intentionally set the IV to collapse the vein to cause Lockett’s suffering.’’ Maj. Op. 1112. True, "deliberate indifference entails something more than mere negligence.” Farmer v. Brennan, 511 U.S. 825, 835, 114 S.Ct. 1970, 128 L.Ed.2d 811 (1994). But “the cases are ... clear that it is satisfied by something less than acts or omissions for the very purpose of causing harm.” Id.