McDonnell said Friday that 42-year-old Robert Gleason Jr. had shown no remorse for the slayings. Gleason has not appealed his sentence or asked the governor for clemency, but McDonnell said he reviewed the case anyway.
Gleason is scheduled to be executed on Wednesday. He has chosen to die by electrocution. Virginia inmates can choose between electrocution and lethal injection.
Gleason was serving life in prison when he killed his cellmate in 2009. He vowed to keep killing unless given the death penalty, then in 2010 he strangling another inmate as he awaited sentencing.
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