Are four Justices ready to grant cert. on the constitutionality of lethal injection protocols?

Thanks to finding this post at How Appealing (which is a sentencing needle in today's filibuster haystack), I see there might be four Supreme Court Justices eager to explore the constitutionality of lethal injection protocols as a method of execution.  (For some background, see this post on the legal attack on lethal injection.)

This issue came up through the last-minute appeals by Vernon Brown, who was executed by the state of Missouri early this morning (details here).  As revealed by this SCOTUS order (on page 3), four Justices voted to issue a last-minute stay; Justice Stevens wrote a brief opinion, joined by Justices Ginsburg and Breyer, explaining that he "would grant the stay for the reasons stated in Judge Bye's dissenting opinion."  (Interestingly, Justice Souter indicated he would grant the stay, but did not sign on to the Stevens opinion.)

The reference to Judge Bye's dissenting opinion concerns the earlier disposition by the Eighth Circuit of Brown's stay application.  A panel denied the motion for a stay in Brown v. Crawford, No. 05-2130 (8th Cir. May 17, 2005) (available here), but Judge Bye wrote a fascinating 8-page dissent focused on Brown's claims about the constitutionality of Missouri's lethal injection protocol.  Here are snippets from Judge Bye's opinion:

Brown challenges the chemical protocol used by Missouri to carry out lethal injections.  He contends the three-chemical sequence used by Missouri — sodium pentothal, pancuronium bromide, and potassium chloride — creates a foreseeable risk of the gratuitous infliction of unnecessary pain and suffering in violation of the Eighth Amendment....

As Brown's district court pleadings indicate, Missouri is "using a combination of chemicals they knew or should have known would cause an excruciating death when they were telling the public it was like putting a dog to sleep, when their own veterinarians would lose their licenses for using the same chemicals on a stray."  Brown v. Crawford, No. 4:05-CV-746-CEJ, Motion for Temporary Restraining Order at 19.  Brown contends there are alternative chemical protocols — for example, a lethal dose of pentobarbital — Missouri could use to carry out an execution without unnecessarily inflicting gratuitous pain and suffering....

Missouri has not countered Brown's medical evidence with any medical evidence of its own, but rather relied solely on procedural and legal defenses to this action.  The state's failure to counter Brown's medical evidence leaves Brown's evidence uncontroverted.  Thus, this case is unlike those in which similar challenges to this three-drug protocol were rejected, because in those cases the state presented medical evidence to counter the prisoner's claim he would be conscious and suffer extreme, unnecessary pain during an execution.  On the current state of this record, where the State of Missouri has not presented any evidence to counter Brown's medical evidence, I believe it is clear Brown is entitled to a stay of his execution.