The justices on Tuesday unanimously upheld Jonathan Ian Burns' death and prison sentences for the January 2007 rape and murder of Jacquelan "Jackie" Hartman. She was shot in the head and her body left in the desert.
Hartman and Burns had met at a gas station and exchanged phone numbers earlier that month.
A jury convicted Burns of first-degree murder, kidnapping, sexual assault and misconduct involving weapons.
The jury ruled that Burns was eligible for the death sentence he received for the murder conviction because he previously was convicted of a serious offense and because the homicide was especially heinous, cruel or depraved.
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