WASHINGTON — The latest capital punishment debate focuses on three things: the trio of drugs used in executions on most state's death rows.

The Supreme Court is delving into a limited part of the subject: whether inmates can file special last-minute challenges to the chemicals used in lethal injection even if they've exhausted all their regular appeals.

The court, which has added two new members since it last dealt with a lethal injection case, was hearing arguments today on behalf of Florida death row inmate Clarence Hill.

Hill, convicted of killing a police officer, 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.

He claims that the chemicals used in Florida executions and by many other states — sodium pentothal, pancuronium bromide and potassium chloride — can cause excruciating pain. The first drug is a pain killer. The second one paralyzes the inmate and the third causes a fatal heart attack.

Justices have never ruled on the constitutionality of lethal injection, which is used by the federal government and every state that has capital punishment except Nebraska.

In this case, they can give inmates new authority to challenge lethal injection as unconstitutionally cruel. The court's decision to hear the case renewed legal efforts around the country on behalf of death row inmates.

If the court allows Hill to file a civil rights action, "it will be a stamp of approval from the United States Supreme Court for these challenges to go ahead," said Deborah Denno, a Fordham Law School professor.

She said the outcome may not reveal much about the new court.

Chief Justice John Roberts replaced the late William H. Rehnquist, and Justice Samuel Alito replaced the retired Sandra Day O'Connor.

O'Connor wrote the court's 2004 ruling in its last lethal injection case. Justices said that Alabama death row inmate David Larry Nelson could pursue a last-ditch claim that his death by lethal injection would be unconstitutionally cruel because of his damaged veins. He argued that prison staff would have to cut into his flesh to get to a vein.

Kent Scheidegger, legal director of the pro-death penalty Criminal Justice Legal Foundation, said, "Hill's failure to follow the rules governing that process should not be rewarded by the opportunity to delay his well-deserved execution."