The procedures cause unconstitutional pain and suffering under the Eight Amendment.  But, these prohibited "cruel and unusual" procedures, the Supreme Court said in Trop v Dulles (1958) should change over time being punishments that offend society's sense of decency.

The case before the Supreme Court was not one directed at the constitutionality of the death penalty itself, but rather, one of the unconstitutionality of the procedure used and contemplated.  Indeed, was one of the drugs deployed in the death protocol pharmacologically capable of avoiding cruel and unusual punishment.

Did the questioned drug's properties affect not only the spinal cord, but also, the brain. Would its central nervous system properties withstand a negating shock from the next drug in the series, potassium chloride?  Would the questioned drug permit the final, lethal drug of the protocol, potassium chloride, to kill without sensing  excruciating pain.  Pain, acknowledged to be akin to being "burned at the stake," albeit from the inside out rather than outside in.  

The record shows that Justices Sotomayor, Kagan, Ginsburg and Breyer understood the issues and the case before them. The conservative justices who spoke demonstrated that they were unprepared or unconcerned, or both. Perhaps, they should look to their colleague Justice Thomas--better to have others think you are unaware than to speak and remove all doubt.