The court's 5-2 ruling rejected arguments that attorneys for Anthony Sowell wasted time challenging evidence against him and should have focused instead on sparing him from capital punishment.
The court also rejected a request for a new, open court hearing to challenge the admissibility of Sowell's hourslong police interrogation.
At issue was a 2010 hearing during which a Cleveland judge closed the courtroom while he heard arguments for and against allowing the videotaped interrogation, which lasted for more than 11 hours.
The judge identified an overriding interest that supported closing that hearing, Justice Terrence O'Donnell said.
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As a result, "the trial court did not abuse its discretion in ordering the limited closure of the courtroom," O'Donnell said.
Justice William O'Neill and Chief Justice Maureen O'Connor dissented, saying a new hearing should be held.
In "a criminal-justice system governed by the rule of law, a serial murderer's trial is subject to the same constitutional protections as the trial of a low-level thief," O'Neill wrote.
Sowell, 57, was indicted in 2009 and convicted and sentenced in 2011. Jurors found Sowell guilty of killing 11 women from June 2007 to July 2009. Police found their mostly nude bodies throughout his home after a woman escaped and said she had been raped in the house.
While Ohio plans three executions next year, it hasn't said if it has enough drugs for additional executions. Two dozen men are on the state's death row.
New lawyers for Sowell argued a better strategy would have been to concede Sowell's overwhelming guilt and push for life without parole based on his background, including a chaotic childhood.