Following are some facts about the case.
* The federal government and all but one of the U.S. states with the death penalty use lethal injection for executions. The only exception is Nebraska, which uses the electric chair.
* Executions in the United States last year at 42 fell to the lowest level in 13 years, mainly as a result of the unofficial moratorium after the Supreme Court decided in late September to rule on the lethal injection case.
* Since 1976, when the Supreme Court reinstated the death penalty, there have been 929 executions by lethal injection, 154 by electrocution, 11 by the gas chamber, three by hanging and two by firing squad. according to the Death Penalty Information Center, which opposes capital punishment.
* Kentucky, the state involved in the case, adopted lethal injection as an execution method in 1998. It has used the method only once -- in 1999.
* The lethal three-chemical cocktail given to death row inmates consists of sodium thiopental, which causes unconsciousness, pancuronium bromide, which results in paralysis, and potassium chloride, which stops the heart.
* The American Civil Liberties Union, Human Rights Watch and other opponents of capital punishment supported the challenge by two death row inmates to the lethal injection method while the Bush administration, a number of states and a group called the Criminal Justice Legal Foundation supported Kentucky.
* The case is the latest of a series dealing with capital punishment that the court has considered in recent years. In 2005, it abolished the death penalty for juveniles, and in 2002 it barred executions of mentally retarded criminals.