The SCOTUS has held, in a 7-2 decision in Baze v. Rees, that lethal injection is constitutional and does not constitute cruel and unusual punishment under the Eighth Amendment. The plaintiffs, both death row inmates, had claimed that it was unconstitutional as cruel and unusual punishment due to possible maladministration of the injections that can or could cause extreme pain. Only Souter and Ginsburg dissented.

Given that the court has long held the death penalty constitutional, I never really felt this outcome of this claim was in doubt. If the DP is to be done, this mode is a long accepted way of doing it more quietly and pain free by odds than other long done methods that are also traditional but not generally overly gruesome, prolonged and/or brutal (drop method hanging, electric chair, gas chamber, firing squad, etc). The Amendment also wasn't, at least by apparent original intent and its wording, intended to guarantee a pain-free execution but rather to prevent strange and barbaric punishments and torturous punishments then used or once used in British punishments (hang, draw and quartering and other gruesome and cruel execution spectacles, Tower of London gruesome torturing, etc).