That decision involved a three-drug method that many states no longer use because certain drugs have been cut off by European suppliers.
More recently, attorneys making the cruel-and-unusual argument have targeted the newer drug combinations adopted around the country, their reliability and their suppliers, but they have had little success.
Making that argument has always been difficult.
The Supreme Court has never declared a method of execution unconstitutional on the grounds that it is cruel and unusual. Over the past 135 years, it upheld the firing squad (1879), the electric chair (1890), and then lethal injection.
The court made it clear over the years that the Eighth Amendment prohibits inflicting pain merely to torture or punish an inmate, drawing a distinction between a method like electrocution and old European practices such as drawing and quartering. The Constitution prohibits "unnecessary and wanton infliction of pain," the court said in 1976.
It has also held that "an isolated mishap" during an execution does not violate the Eighth Amendment, "because such an event, while regrettable, does not suggest cruelty or a 'substantial risk of serious harm,'" according to a 1947 decision allowing Louisiana to return an inmate to the electric chair after a botched attempt a year earlier.
That suggests that an isolated episode — say, one bungled execution in Oklahoma — might not be enough to bring the issue before the Supreme Court.
But if it can be shown that there's a pattern, "at some point the court's going to have to look at it," said Dale Baich, a federal public defender in Arizona who has represented death row inmates.
States have botched several executions previously, leading at times to changes in execution policies but no widespread prohibition.
In 2000, Florida switched from the electric chair to injection after bungled electrocutions raised concerns that the state's death penalty would be declared unconstitutional.