Meanwhile, two of the justices said for first time that death penalty itself probably is unconstitutional.
The justices voted 5-4 in a case from the state of Oklahoma that the sedative midazolam can be used in executions without violating a constitutional prohibition on cruel and unusual punishment.
The drug used in executions in Arizona, Ohio and Oklahoma in 2014 took longer than usual and raised concerns that it did not perform its intended task of putting inmates into a coma-like sleep.
Executions have been on hold in Ohio since a troubling 26-minute execution in 2014 during which a prisoner getting a first-ever two-drug combo repeatedly gasped and snorted.
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Last year, Arizona officials were cleared of any wrongdoing in an execution that lasted nearly two hours, but they nevertheless changed the drugs they use to put inmates to death.
Justice Samuel Alito said for a conservative majority Monday that arguments the drug could not be used effectively as a sedative in executions is speculative.
Alito responded, saying "the dissent's resort to this outlandish rhetoric reveals the weakness of its legal arguments."
In a separate dissent, Justice Stephen Breyer said the time has come for the court to debate whether the death penalty itself is constitutional. Another justice joined that opinion.
The Supreme Court's involvement in the case began in January with an unusually public disagreement among the justices over executions.