PHOENIX - The U.S. Supreme Court on Tuesday refused to give Scott Nordstrom another chance to escape the death penalty.

Without comment, the justices rejected his plea for a new sentencing for multiple shooting deaths during a pair of 1996 robberies in Tucson. That leaves Nordstrom on death row.

Nordstrom was not challenging the conviction itself.

Nordstrom and Robert Jones were charged with killing two men while robbing the Moon Smoke Shop. Two weeks later, they shot and killed four people during a robbery at the Firefighters' Union Hall, a social club. Both were sentenced to death.

But in 2002, the U.S. Supreme Court, ruling in another Arizona murder case, said the death penalty cannot be imposed solely by a judge, if a defendant objects. The justices said defendants are entitled to make their case for being spared to a jury.

In 2009, a jury resentenced him to die.

In his petition to the nation's high court, Nordstrom said it was wrong for the judge presiding over the resentencing to preclude him from introducing evidence from his original trial he claimed would show his innocence. The judge in that case said such evidence is inadmissible for purposes of sentencing.

The Arizona Supreme Court already had rejected Nordstrom's argument.

Both robberies were solved when Scott's brother, David Nordstrom, contacted police. He had been the driver in the getaway vehicle.

Jones' death sentence imposed by a judge was upheld before that 2002 U.S. Supreme Court ruling. He remains on death row.

Note: As of May 30, 2016, Scott Nordstrom is still on Death Row.