WASHINGTON (AP) – The Supreme Court opened the door Monday to new constitutional challenges to lethal injection, the method used by most states and the federal government to execute death row inmates.

In an unanimous decision, the court allowed those condemned to die to make last-minute claims that the chemicals used are too painful _ and therefore amount to cruel and unusual punishment in violation of the Constitution’s Eighth Amendment.

Justices, in a separate 5-3 ruling, also made it easier for death row inmates to challenge their convictions with new evidence. The court said Tennessee death-row inmate Paul Gregory House can use DNA evidence to try to get his conviction overturned in the 1985 murder of a neighbor.

“This is not a case of conclusive exoneration,” Justice Anthony M. Kennedy wrote in the decision, which permits House to proceed in federal court claiming innocence for the murder of Carolyn Muncey in Union County, Tenn., in July 1985.

The lethal injection ruling sets the stage for a nationwide legal battle over that subject, with the country’s 3,300 death row inmates armed with a new tool to contest how they are put to death. Justices have never ruled on the constitutionality of a specific type of execution.

The winner in the case was Florida death row inmate Clarence Hill, who was strapped to a gurney with lines running into his arms to deliver the drugs when the Supreme Court in January intervened and blocked the execution.

Kennedy, writing for the court, said that while Hill and other inmates can file special appeals, they will not always be entitled to delays in their executions.

“Both the state and the victims of crime have an important interest in the timely enforcement of a sentence,” he wrote.

Hill, convicted of killing a police officer, had run out of regular appeals so he went to court using a civil rights law claiming that his constitutional rights would be violated by Florida’s lethal injection drug protocol. The court’s decision renews his bid to have Florida change its chemical combination.

The decision is setback for Florida and other states that will have to defend more last-minute filings from inmates. More than two dozen states had filed arguments at the court seeking the opposite outcome. They said dragged-out appeals jeopardize justice for victims’ families.

Lethal injection is the main method used by every state that has capital punishment except Nebraska. Nebraska still has the electric chair, although that, too, is being contested.

Kennedy said that Hill is not claiming that he cannot be executed, only that he should not be forced into a painful execution.

“Hill’s challenge appears to leave the state free to use an alternative lethal injection procedure,” Kennedy wrote.

Justices seemed worried about the possibility of pain when they took up Hill’s case in April. Justice John Paul Stevens told Florida’s lawyer that their procedure would be banned for use to euthanize cats and dogs.

Following the Supreme Court’s intervention in the Hill case, executions were stopped in California, Maryland and Missouri.

Hill’s lawyer, D. Todd Doss, said Monday that the state can revise its method or try to defend its system in court.

“It is a good day in the sense that we get to litigate on the merits of this. We have an opportunity to litigate an execution claim,” he said.

Retired Justice Sandra Day O’Connor wrote the court’s 2004 ruling in its last lethal injection case. Justices said then that an Alabama death row inmate could pursue a last-ditch claim that his death by lethal injection would be unconstitutionally cruel because of his damaged veins.

In Monday’s ruling, Kennedy wrote that the court was only following precedent set in that case.

The case is Hill v. McDonough, 05-8794.