Updated

An Oklahoma appeals court on Thursday upheld the death penalty of a man convicted of killing his girlfriend and her two children then burning their mobile home in 2010.

The court ruled that testimony by the victims' relatives saying Shaun Bosse should be executed should not have been allowed, but was harmless error because of other evidence.

Bosse, 34, was convicted on three counts of first-degree murder and arson in the deaths of 25-year-old Katrina Griffin, 8-year-old Christian Griffin and 6-year-old Chasity Hammer. Their bodies were found July 23, 2010, in their burned mobile home in Dibble, about 40 miles (64 kilometers) south of Oklahoma City.

"Overwhelming evidence supports the conclusion that all three murders were heinous, atrocious or cruel," Judge Clancy Smith wrote in the ruling.

Bosse's attorney, Michael Morehead, did not return a phone call seeking comment.

Autopsy reports say Katrina and Christian were stabbed to death, while Chasity died of smoke inhalation and burns. Prosecutors said she was trapped in a closet, with the door blocked by a chair.

Prosecutors say Bosse was linked to the crimes in part by pawn tickets found in his wallet showing that, while the home was still burning, he sold more than 100 items taken from it to various pawn shops in Oklahoma City.

The ruling, and a separate opinion by Presiding Judge Gary Lumpkin, noted that 23 witnesses testified on behalf of Bosse, including 14 who asked that his life be spared.

"In light of other evidence at trial, including the numerous individuals requesting mercy on behalf of Appellant, the (victims') witnesses' recommendations were harmless beyond a reasonable doubt." Lumpkin wrote.

"I'm happy for this part of the process to be over for the victims' family and be one step closer to, hopefully, getting some closure," said District Attorney Greg Mashburn.

The court had previously rejected Bosse's appeal that the relatives' testimony was improper, citing a U.S. Supreme Court ruling, but the high court ruled in October that the testimony during Bosse's sentencing should not have been allowed and sent the case back to the Oklahoma court.