Georgia moved quickly Wednesday to clear the way for the execution of two condemned killers after the U.S. Supreme Court upheld the constitutionality of lethal injection.

Just hours after the U.S. Supreme Court ruled that Kentucky's lethal-injection method does not violate the Eighth Amendment's guarantee against cruel and unusual punishment, Georgia Attorney General Thurbert Baker asked that stays be lifted to allow the executions of Jack Alderman and Curtis Osborne.

Their executions were put on hold in October by the Georgia Supreme Court because the lethal-injection challenge was pending before the U.S. Supreme Court.

The U.S. Supreme Court's splintered, 7-2 decision effectively ended a de facto moratorium on capital punishment nationwide. Georgia, like Kentucky, uses a three-drug cocktail to execute death-row inmates.

Alderman awaits execution for killing his wife in 1974 in Chatham County. Osborne sits on death row for a 1990 double murder in Griffin.

Alderman already is challenging the constitutionality of lethal injection in a federal lawsuit filed in Atlanta.

One of his lawyers, Michael Siem, said Wednesday that nothing in the high court's ruling counters Alderman's contention that lethal injection procedures in Georgia are unconstitutional. "As such, we continue to press the state of Georgia to make the changes necessary to ensure constitutional executions," Siem said.

Siem filed a federal court motion Wednesday saying there are key differences between lethal injection in Kentucky and Georgia. "The Georgia procedures lack basic safeguards to prevent an inmate from suffering substantial harm," the motion said.

Of the 36 states that allow the death penalty, 27 — including Georgia — require lethal injection as the sole method of execution.

Chief Justice John Roberts on Wednesday announced the high court's decision.

Roberts noted that the two death-row inmates from Kentucky who mounted the challenge acknowledge that lethal injection, if applied as intended, will result in a humane death.

Much of the inmates' case rested on their contention that the three-drug cocktail posed a potential risk of excruciating pain because the protocol for administering it might not be properly followed. They also proposed an alternative protocol.

"We cannot say that the risks identified by [the condemned inmates] are so substantial or imminent as to amount to an Eighth Amendment violation," Roberts wrote. Also, "a condemned prisoner cannot successfully challenge a state's method of execution merely by showing a slightly or marginally safer alternative."

In 1976, in the case Gregg v. Georgia, the high court upheld the constitutionality of the death penalty.

"It necessarily follows that there must be a means of carrying it out," Roberts wrote. "Some risk of pain is inherent in any method of execution — no matter how humane — if only from the prospect of error in following the required procedure. It is clear, then, that the Constitution does not demand the avoidance of all risk of pain in carrying out executions."

Throughout U.S. history, society has steadily moved to more humane methods of execution, Roberts wrote. The firing squad, hanging, the electric chair and the gas chamber have each given way to more humane methods, culminating in a consensus on lethal injection.

The high court never struck down one of those methods, Roberts said, noting that nothing has stopped legislatures from taking steps to ensure more humane methods of execution. "There is no reason to suppose that today's decision will be any different," he said.

Justices Anthony Kennedy and Samuel Alito agreed with Roberts' opinion. Alito also wrote a separate concurring opinion, as did four other justices, to give the court its seven-vote majority.

One of them was Justice John Paul Stevens, who wrote for the first time that he believes the death penalty is unconstitutional. But Stevens said he would continue to respect the court's precedents upholding capital punishment and agreed with the court that the Kentucky inmates did not prove lethal injection was cruel and unusual punishment.

Stevens said he had hoped the court's decision would bring the debate about the lethal injection to a close.

"It now seems clear that it will not," Stevens wrote. "The question whether a similar three-drug protocol may be used in other states remains open" and could be decided differently in another case with more evidence, he said.

But Roberts responded, saying that a stay of execution may be granted only when a condemned prisoner establishes a demonstrated risk of severe pain.

"A state with a lethal injection protocol substantially similar to the [Kentucky] protocol we uphold today would not create a risk that meets this standard," Roberts said.

Justices Ruth Bader Ginsburg and David Souter, dissented. Ginsburg said she would ask Kentucky courts to consider whether the state includes adequate safeguards to ensure an inmate is unconscious and unlikely to suffer severe pain.

Georgia was not the only state to respond quickly to the decision. Virginia Gov. Tim Kaine, who suspended executions as the high court considered the lethal injection challenge, said Wednesday that Virginia can resume executions of condemned killers.

In Georgia, a third death-row inmate, William Lynd, who was sentenced to death for the 1988 murder of his live-in girlfriend in Berrien County, may also get a death warrant soon. Lynd's appeals were exhausted last year, making him eligible for a death warrant. None was sought, however, when it became clear there was a de facto moratorium until the U.S. Supreme Court decided the lethal injection challenge.

The Associated Press and Washington Post contributed to this story.