Scott Peterson’s conviction for killing his pregnant wife will stand, but the California Supreme Court on Monday overturned his 2005 death sentence in a case that attracted worldwide attention. The justices cited “significant errors” in jury selection in overturning the death penalty but welcomed prosecutors to again seek the sentence if they wish.

Laci Peterson, 27, was eight months pregnant with their unborn son, Connor, when she was killed. Investigators said that on Christmas Eve 2002, Peterson dumped their bodies from his fishing boat into San Francisco Bay, where they surfaced months later.

“Peterson contends his trial was flawed for multiple reasons, beginning with the unusual amount of pretrial publicity that surrounded the case,” the court said. “We reject Peterson’s claim that he received an unfair trial as to guilt and thus affirm his convictions for murder.”

But the justices said the trial judge “made a series of clear and significant errors in jury selection that, under long-standing United States Supreme Court precedent, undermined Peterson’s right to an impartial jury at the penalty phase.”

It agreed with his argument that potential jurors were improperly dismissed from the jury pool after saying they personally disagreed with the death penalty but would be willing to follow the law and impose it.

“While a court may dismiss a prospective juror as unqualified to sit on a capital case if the juror’s views on capital punishment would substantially impair his or her ability to follow the law, a juror may not be dismissed merely because he or she has expressed opposition to the death penalty as a general matter,” the justices said in a unanimous decision.

They rejected Peterson’s argument that he couldn’t get a fair trial because of widespread publicity after the proceedings were moved nearly 90 miles (145 kilometers) away from his Central Valley home of Modesto to San Mateo County, south of San Francisco.