He was condemned for the February 2005 deaths of Lisa Underwood, 34, and her son Jayden.
Texas prison officials didn’t formally update their policy but said they would review inmates’ petitions on a case-by-case basis and would grant most reasonable requests.
Prosecutors said Barbee killed his ex-girlfriend and her son because he didn’t want his wife to know Underwood was seven months pregnant, presumably by him.
Barbee confessed to police he killed Underwood and her son but later recanted.
If Barbee is executed, he would be the fifth inmate put to death this year in Texas.