An Arizona man convicted of murder in the 1984 killing of an 8-year-old girl was put to death Wednesday in the state’s second execution since officials resumed carrying out the death penalty in May following a nearly eight-year hiatus.

Frank Atwood, 66, died by lethal injection at the state prison in Florence for his murder conviction in the killing of Vicki Lynne Hoskinson, whose body was found in the desert, Arizona Attorney General Mark Brnovich said in a statement.

Vicki Lynne went missing months earlier after leaving her home in Tucson to drop a birthday card in a nearby mailbox.

The U.S. Supreme Court cleared the way for Atwood’s execution Wednesday morning after rejecting a final appeal by his lawyers. He died at 10:16 a.m., Brnovich said, and witnesses reported that the execution went smoothly.

Atwood was the second Arizona prisoner to be put to death in less than a month. The execution of Clarence Dixon in May ended Arizona’s halt to executions that was blamed on the difficulty of obtaining lethal injection drugs and criticism that a 2014 execution in the state was botched.

Death penalty opponents now worry that Arizona will now start executing a steady stream of prisoners who have languished on death row, but state officials didn’t provide details when asked about the state’s future execution plans.