Justice David Souter urged his colleagues to take the time necessary to issue a definitive decision about the three-drug method in this case, even if it means sending the case back to Kentucky for more study by courts there.

Scalia, however, said such a move would mean “a national cessation of executions. We’re looking at years. We wouldn’t want that to happen.”

Kentucky, backed by the Bush administration, says it works hard to execute inmates humanely, countering claims that its procedure violates a constitutional ban on cruel and unusual punishment.

But Donald Verrilli, a Washington lawyer who is a veteran of death penalty cases, told the justices that problems with executions in California, North Carolina and other states show that the three-drug procedure should be scrapped or thoroughly revamped.

“The risk here is real. That is why it is unlawful to euthanise animals the way Kentucky executes inmates,” Verrilli said. Kentucky bars the use of the paralytic on animals. An overdose of barbiturates is commonly used on animals.