TALLAHASSEE, Fla. (AP) — A man convicted of raping and murdering a woman 32 years ago in St. Petersburg lost a bid Wednesday for a stay of his execution that’s scheduled for next week.

The Florida Supreme Court rejected arguments by 65-year-old Robert Waterhouse that he should be spared because of testimony from a newly discovered witness and the destruction of physical evidence that made it impossible to perform DNA testing that could exonerate him.

Waterhouse’s execution by lethal injection is set for next Wednesday at Florida State Prison in Starke. Gov. Rick Scott signed his death warrant.

The former plasterer and drywall worker was convicted of beating 29-year-old Deborah Kammerer with what was believed to be a tire iron and then leaving her to drown in  Tampa Bay. Her nude body was found in the bay’s mud flats in January 1980.

The justices issued a unanimous, unsigned 47-page opinion just a day after hearing oral argument.

They concluded the new testimony was unreliable and wouldn’t have been enough to acquit Waterhouse if he were to be retried.

“In light of Waterhouse’s incriminating statements and other evidence of his guilt, this cumulative testimony cannot ‘reasonably be taken to put the whole case in such a different light as to undermine confidence in the verdict,’” the justices wrote, quoting a 1999 U.S. Supreme Court ruling.

Blood was found in Waterhouse’s car and at least one witness saw him leaving a bar with the victim on the night she was killed. Waterhouse, who was on parole for the 1966 murder of a 77-year-old New York woman, told detectives that when he drinks a lot, as he did on the night of Kammerer’s murder, he cannot control his behavior.

The justices rejected the destroyed evidence argument as untimely, procedurally barred and improperly pleaded. They noted they had rejected a similar claim from Waterhouse in 2006 and that he could cite no other case establishing a fundamental right to relief because evidence had been destroyed after a conviction.

Waterhouse’s lawyer, Robert Norgard, did not immediately return an after-hours phone message left at his Bartow office. Norgard previously has said he likely would file additional challenges in the federal court system.

The new witness, Leglio Sotolongo, was a doorman at the ABC Lounge at the time of the murder. He testified that he saw Waterhouse leave with two men, not the victim, on the night she was killed.

The justices pointed out that another employee offered similar but more detailed testimony, yet that did not sway the jury.

The high court agreed with a judge who heard Sotolongo’s testimony that it was not reliable, noting he could not remember if he was working on the night of the murder and had qualified his statement as being true as far as he “could recall.”

Justice Peggy Quince did not participate in the decision. She is a former assistant attorney general who once worked on the case.

The case is Robert Brian Waterhouse v. State of Florida, No. SC12-107.

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Associated Press writer James L. Rosica contributed to this report.