PATRICK E. HIGGINBOTHAM, Circuit Judge:

In 2012, Texas adopted its current execution protocol: a single, five-gram dose of pentobarbital to induce death. Five men convicted of murder and sentenced to die by lethal injection ask this Court to stay their impending executions based on an earlier and separate case between Texas and two death row prisoners. Three of the five received stays from the Texas Court of Criminal Appeals on state habeas petitions presenting claims not at issue here. The remaining two argue that Texas is obliged by the Eighth Amendment's prohibition on cruel and unusual punishment and the Fourteenth Amendment's guarantee of equal protection under the law to re-test the execution drug to assure it does not present a high risk of unnecessary pain. We are not persuaded these prisoners have made the showing required for a stay pending appeal and DENY their motion for a stay of execution.

I.

A.

Appellants filed this 42 U.S.C. § 1983 civil suit on August 12, 2016 in the United States District Court for the Southern District of Texas, alleging violations of the First, Eighth, and Fourteenth Amendments, and sought a preliminary injunction that would have granted the ultimate relief requested in the complaint. They asserted that: (1) Texas's use of compounded pentobarbital absent re-testing shortly before execution violates the Eighth and Fourteenth Amendments by creating a substantial risk of severe pain; (2) Texas's refusal to disclose elements of its execution protocol violated Appellants' First, Eighth, and Fourteenth Amendment rights to be free from cruel and unusual punishment, due process, notice, an opportunity to be heard, and access to the courts; (3) voluntary re-testing of the pentobarbital that will be used to execute plaintiffs in another suit created a constitutional right to such re-testing for all prisoners; and (4) the lack of a requirement that Texas notify the Appellants of any changes to the drugs or to the lethal injection protocol that will be used to carry out their sentences impairs protection of their right to be free from cruel and unusual punishment and to due process under the Eighth and Fourteenth amendments.

The State moved to dismiss the complaint on August 15, 2016, arguing that all except the equal protection claim were time-barred and all claims failed as a matter of law. At a hearing the following day, the district court denied the request for a preliminary injunction and dismissed the complaint for failure to state a claim. The next day the district court denied a stay pending appeal.

B.

The prisoners' suit now before us presents as the latest in a series of cases targeting capital punishment. In the recent case before this court of Jordan v. Fisher, a group of Mississippi death row inmates challenged that state's use of pentobarbital as the first drug in a so-called "three-drug cocktail."1 There, the Jordan prisoners complained to the district court that pentobarbital was not a sufficiently fast acting barbiturate to guarantee anesthetization prior to the introduction of vecuronium bromide and potassium chloride, urging as the alternative a single, lethal dose of a barbiturate.

Since 2012 the State of Texas has done just that — execution via a single-drug protocol utilizing a five-gram dose of pentobarbital. Texas originally used pentobarbital purchased from a pharmaceutical firm in its executions. However in 2011, Lundbeck, the Danish pharmaceutical firm that produces manufactured pentobarbital, refused to supply the drug to states that execute by lethal injection.2 In response, in September 2013, Texas began purchasing pentobarbital compounded by pharmacies.3 Texas alleges, and Appellants do not dispute, that Texas has used compounded pentobarbital to execute thirty-two prisoners since 2013 without issue. Even so, Appellants' primary contention is that Texas's use of compounded pentobarbital creates significant risks of unnecessary pain, and thus the state should be compelled to re-test the drug shortly before execution.

II.

A.

Appellants request a stay of execution pending review in this Court of the district court's dismissal of their suit and denial of a stay pending appeal. A stay of execution is an equitable remedy that is not available as a matter of right.4 In determining whether to grant a stay pending appeal, this Court weighs:

B.

"[B]ecause it is settled that capital punishment is constitutional, `[i]t necessarily follows that there must be a [constitutional] means of carrying it out.'"6 The Court has repeatedly held that lethal injection is a permissible method of execution.7 While the Eighth Amendment does not require that execution be painless,8 it does prohibit "serious illness and needless suffering" where there exists an alternative that is "feasible, readily implemented, and in fact significantly reduce[s] a substantial risk of severe pain."9 The Amendment secures a right to be free from methods of execution that create "a risk that is sure or very likely to cause serious illness and needless suffering, and give rise to sufficiently imminent dangers."10 Stated differently, "there must be a substantial risk of serious harm, an objectively intolerable risk of harm that prevents prison officials from pleading they were subjectively blameless for purposes of the Eighth Amendment."11

C.

The Equal Protection Clause of the Fourteenth Amendment is "essentially a direction that all persons similarly situated should be treated alike."12 Its basics are rote: "[e]qual protection does not require that all persons be dealt with identically, but it does require that a distinction made have some relevance to the purpose for which the classification is made."13 In assessing an equal protection claim, "[s]trict scrutiny is appropriate only where a government classification implicates a suspect class or a fundamental right."14 "In cases that do not implicate suspect classes or fundamental rights, `[t]he appropriate standard of review is whether the difference in treatment between [classes] rationally furthers a legitimate state interest.'"15 "Under rational basis review, differential treatment must be upheld against equal protection challenge if there is any reasonably conceivable state of facts that could provide a rational basis for the classification."16

An equal protection claim that is premised on differential treatment but not based on membership in a suspect class or the infringement of a fundamental right may be cognizable as a so-called "class of one."17 "We review such claims under a two-prong test: the plaintiff must show that (1) he or she was intentionally treated differently from others similarly situated and (2) there was no rational basis for the difference in treatment."18

III.

Each of these men was sentenced to death over a decade ago — two more than twenty years ago — and each has known he will be executed using compounded pentobarbital since at least 2013. In moving for a stay, the prisoners assert only their equal protection claim; other claims in the complaint are not before us.

A.

The first requirement for a stay of execution is "a strong showing that [the movant] is likely to succeed on the merits."19 We examine the alleged errors of the district court for a substantial likelihood of success before this Court.

i.

The prisoners first argue that the Eighth Amendment right to be free from cruel and unusual punishment is burdened by Texas's denial of re-testing shortly before execution. They urge that the district court erred by evaluating their claim under rational basis review; that the correct standard of review is strict scrutiny, with a shift of the burden to the State to demonstrate that its classification was narrowly tailored to achieve a compelling government interest.

This argument relies on the contention that Texas's decision to re-test the pentobarbital in the Whitaker20 case and not here denies them equal protection. In Whitaker, the plaintiffs, as here, alleged that Texas does not provide all of the procedural safeguards they believed necessary for the use of compounded pentobarbital. While all agreed that Texas's decision to re-test mooted the case,21 the district court dismissed the suit for other reasons.22 The prisoners' primary contention now is that re-testing in Whitaker created a right to re-testing for all prisoners, a novel and flawed invocation of equal protection doctrine.

The Eighth Amendment guarantees a right to be free from methods of execution that present a substantial risk of unnecessary pain. That right is enjoyed by all persons. It rests on text, not on episodic differential treatment. In Glossip, the Court held that a method of execution does not violate the Eighth Amendment unless it "presents a risk that is sure or very likely to cause serious illness and needless suffering, and give rise to sufficiently imminent dangers."23 The Court held that, to qualify for a stay of execution, plaintiffs must demonstrate "that the State's lethal injection protocol creates a demonstrated risk of severe pain."24 These are substantial hurdles, necessarily so.

Appellants assert that there is a risk that the drug might fail, and thus re-testing for one and not another impinges upon the Eighth Amendment. That said, under Glossip, the prisoners must establish that not re-testing the drug presents a sure or very likely risk of pain.

The reality is that pentobarbital, when used as the sole drug in a single-drug protocol, has realized no such risk. The prisoners cannot avoid the facts that: (1) the district court found that at least thirty-two executions in Texas have utilized the single-drug compounded pentobarbital protocol without incident25 and, (2) when pentobarbital is the sole drug used to execute, unconsciousness necessarily precedes death,26 effectively obviating the problem of conscious pain and suffering that was oft cited as a risk of the "three-drug cocktail." Rather, relying on conjecture regarding the drugs' beyond-use dates and compounding, the prisoners urge only that "[t]esting the compounded pentobarbital shortly before its use ensures the prisoner will not suffer severe pain...." But this assertion fails to reach the Eighth Amendment bar on unnecessarily severe pain that is sure, very likely, and imminent. The effort to draw upon equal protection works no change in the reach of the Eighth Amendment.

However one kneads the protean language of equal protection jurisprudence, the inescapable reality is that these prisoners have not demonstrated that a failure to retest brings the risk of unnecessary pain forbidden by the Eighth Amendment. Attempting to bridge this shortfall in their submission with equal protection language, while creative, brings an argument that is ultimately no more than word play.

ii.

The prisoners do not allege membership in a protected class, and despite efforts to reframe the issues,27 their claims present at bar as a futile effort to assert a "class of one."

Typically, a class of one involves a discrete group of people, who do not themselves qualify as a suspect class, alleging the government has singled them out for differential treatment absent a rational reason. Olech involved just those facts, with a municipality demanding a 33-foot easement from the plaintiff where it required only a 15-foot easement from other similarly situated property owners.28 Here, the prisoners allege that the Whitaker plaintiffs were singled out to receive a benefit denied to them, turning the Olech analysis on its head.

That problem aside, in Engquist, the Court discussed "forms of state action ... which by their nature involve discretionary decisionmaking based on a vast array of subjective, individualized assessments."29 Engquist dealt with a government employee who brought a class of one claim alleging that her termination violated the Equal Protection Clause.30 At trial, the jury returned a verdict for the plaintiff.31 The Ninth Circuit reversed, and the Supreme Court affirmed the Ninth Circuit's reversal, holding that "ratifying a class-of-one theory of equal protection in the context of public employment would impermissibly `constitutionalize the employee grievance.'"32

The Court recognized that, in the core areas of equal protection, governmental discretion could be used as a cover for impermissible discrimination.33 But here, "treating like individuals differently is an accepted consequence of the discretion granted," and allowing equal protection claims on such grounds "would be incompatible with the discretion inherent in the challenged action."34 The strategic decision of the State of Texas to re-test in one case, in the context of an ever-changing array of suits attacking its use of capital punishment from all angles, is within the discretion inherent in the challenge made here.

The district court held that the Engquist exception to class of one claims controls regarding decisions made, here and in Whitaker, by Texas as a litigant; that, as a matter of law, Appellants' equal protection claim fails as a class of one claim. We agree.

iii.

The prisoners' final contention in support of a stay is that the district court erred in two ways when granting the State's motion to dismiss: procedurally by applying the wrong pleading standard and substantively by dismissing a complaint that "adequately plead an equal protection violation." They argue that the district court "repeatedly challenged Appellants' allegations and factual support" instead of applying the correct standard, under Twombly and Iqbal, which accepts factual allegations in the complaint as true and evaluates the complaint for plausibility.35 The prisoners relied upon two affidavits of proffered expert opinion in support of their motion for a preliminary injunction and then their request for a stay. The district court dispatched them as "junk science." That aside, the affidavits do not themselves move beyond speculation and do not confront the success of pentobarbital as the sole-drug used to execute.

As we earlier explained, the district court found that counts one, two, and four in the complaint are time barred, and that holding is not challenged. Count three, the equal protection claim, fails as a matter of law for the reasons we have stated here — essentially the same reasons offered by the district court. Accepting the facts as pled, all claims still fail. Any error committed is harmless.

B.

Again, of course, "[i]n a capital case, the possibility of irreparable injury weighs heavily in the movant's favor."36 The prisoners argue the injury they will face is the possibility of severe pain during their executions, but they do not demonstrate that they are nigh sure to suffer unnecessary pain. Texas, on the other hand, proffers that compounded pentobarbital has been used in thirty-two executions in the state without issue.37 We cannot say that Appellants have demonstrated that they are likely to suffer an irreparable injury absent a stay.

C.

Texas has a strong interest in enforcing the judgments of its courts in criminal cases, but the public interest writ large takes no sides here. The finality of a death sentence and, with it, the inherent risk of uncertainty demand diligent effort by all. These prisoners have enjoyed that effort — with two of them residing on death row in excess of twenty years. That reality may give pause to the entire enterprise, but does not bespeak neglect of bench and bar. To these eyes, a system that leaves persons on death row for over two decades more surely taxes the Eighth Amendment's prohibition of undue suffering than does the elusive search for minimum pain for those brief moments of passage across the river.

Appellants do not contest their convictions or their sentences. Instead they argue that the Eighth and Fourteenth Amendments require the State of Texas to re-test the pentobarbital that will be used to execute them. The district court determined that Appellants' claims are meritless. Appellants have not made the requisite showing that would justify a stay pending appeal. Appellants' motion for a stay is DENIED.

Concurrence:

JAMES L. DENNIS, Circuit Judge, concurs in denying the motion for a stay.