CENTENNIAL, Colo.  | Lawyers for the Colorado theater shooting suspect want heightened standards of fairness and reliability applied throughout his case, now that prosecutors say they intend to seek the death penalty.

James Holmes’ lawyers said in court documents filed Monday that they want a hearing on the issue. They say prosecutors oppose their arguments.

Holmes is accused of killing 12 people and injuring 70 in a theater attack July 20.

His attorneys say heightened standards are constitutionally required in death penalty cases at trial, not just during sentencing, so that there is certainty that a jury’s verdict is sound. They mention an Alabama death-penalty case in which the U.S. Supreme Court said unreliability was introduced when jurors weren’t told they could’ve convicted a defendant of a lesser offense.