JACKSONVILLE, Fla. – A convicted cop killer, Clarence Hill, was already strapped to a gurney with IV tubes running into his arms to deliver the lethal injection. The executioner was ready for the order to start the flow of drugs, and witnesses including both his family and relatives of the slain police officer were waiting.

But at the last minute, Hill was granted a stay of execution by the U.S. Supreme Court.

On Wednesday, the high court will hear Hill’s appeal, using his case to clarify how inmates may bring deadline challenges to the use of lethal in jection and whether his challenge can be filed as a civil rights action.

How the court rules could decide whether Hill will be executed this summer or whether he will be allowed to challenge Florida’s use of lethal injection as cruel and unusual punishment – a ruling that could halt executions in Florida and perhaps elsewhere, at least temporarily.

Hill’s stay of execution also halted the death of another Florida inmate on the same grounds, and Governor Jeb Bush said he would not sign any other death warrants until Hill’s case is settled.

Hill’s stay also is directly responsible for execution delays in three more cases in other states, a spokesman for the Death Penalty Information Center in Washington, Rion Dennis, said.

A death appeals lawyer in the state attorney general’s office, Carolyn Snurkowski, will argue that Hill cannot challenge Florida’s method of execution through a civil rights action. She also argues he filed his claim against lethal injection too late, since he waited until just before his scheduled execution on January 24.

Hill’s lawyer, D. Todd Doss, argues that the doses of drugs used in Florida executions can cause pain, in violation of the constitutional protection against cruel and unusual punishment.

Hill was convicted of killing a Pensacola police officer, Stephen Taylor, in 1982.

Taylor, 26, and Officer Larry Bailly had gone to investigate a silent alarm at a bank in downtown Pensacola, and caught Hill’s partner, Cliff Jackson, outside the bank. As the officers attempted to handcuff Jackson, Hill came up from behind, killing Taylor and wounding Bailly. Hill was shot five times. Jackson was sentenced to life in prison.

Hill also has claimed he should not be executed since he is mentally retarded.That argument was rejected by the state Supreme Court, which noted that a mental evaluation showed his IQ was 16 points higher than the standard of 70 or below.

Taylor’s family is growing weary after 24 years of delays, his older brother, Jack Taylor, said. They want Hill dead and they were angry when his execution was halted.

However, a cousin of Taylor, Gary Mace of Key Largo, was not upset the high court took the case. “We are willing to see what the courts have to say. I want the Supreme Court to look at this case and make a judicial decision so others won’t have to go through what we went through,” Mr. Mace said.