SALT LAKE CITY — A Utah death-row inmate whose double-murder case was made famous by the book “Under the Banner of Heaven” is one step closer to execution by firing squad after a judge handed down a pair of court defeats Wednesday.

Ron Lafferty was convicted in the 1984 slayings of his sister-in-law Brenda Lafferty and her baby daughter after she resisted her husband’s entry into a polygamous group.

His lawyers say his case was tainted by a graphic videotape of the victims’ bodies shown during sentencing, mistakes by his previous attorneys and bias in the jury, among other problems. They wanted to gather evidence to back up the claims, but their requests have now been denied by U.S. District Judge Dee Benson.

Benson ruled that lawyers waited nearly a decade to make the claims, and the effort to gather new evidence might be pointless.

His lawyers didn’t immediately return messages seeking comment.

Lafferty was convicted along with his brother Dan Lafferty in the deaths of their sister-in-law and her child.

Ron Lafferty claimed to have had a religious revelation sanctioning the slayings because of the victim’s resistance to his beliefs in polygamy. Dan Lafferty is serving a life prison sentence in the case chronicled in Jon Krakauer’s 2003 book about radical offshoots of The Church of Jesus Christ of Latter-day Saints.

If Ron Lafferty’s motions had been granted, the process could have added years to the case, said Andrew Peterson with the Utah Attorney General’s Office.

“This definitely does bring things closer to a conclusion,” he said.

The federal judge also denied Lafferty’s claims last year that the use of the firing squad is cruel and unusual.

Shortly after Utah became the only state to approve the use of a firing squad as a backup if lethal injection drugs are unavailable, Benson ruled that that the U.S. Supreme Court has never overturned a state’s chosen method of execution as unconstitutional.

Ron Lafferty, 75, had argued that the firing squad would cause a lingering, unnecessarily painful death. He chose to die that way when he was sentenced 30 years ago and the choice was available, but his lawyers later argued that he wasn’t legally competent to do so.

He is one Utah’s longest-serving death-row inmates, but a possible execution date could still be years away.