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Chief Justice Roberts (who got Justices Kennedy and Alito to agree, while no other opinion was joined by more than one other Justice) says that a method of execution is only unconsitutional if there is a "substantial risk of serious harm". Here there is a risk, but it is not substantial. The challengers did show that there are ways the injection procedure could be administered improperly, causing severe pain, but they did not establish that the risk was common. Existence of safe alternative execution methods doesn't help, either, especially since the proposed alternatives are untested; no one could say for certain that the alternatives would be significantly better.

Justice Stevens has a long opinion discussing the death penalty and how it's changed over time. He concludes, however, that the Supreme Court's prior holdings establish that the death penalty is constitutional, and he therefore holds that lethal injection is constitutional.

Justice Scalia criticizes Justice Stevens's opinion, saying none of what he says has anything to do with the text of the Constitution.

Justice Thomas, joined by Scalia, says Roberts's opinion looking for "substantial risk of severe harm" has no basis in the text of the Constitution.

Justice Breyer doubts studies showing lethal injection causes pain and doubts availability of better alternatives.