Defense attorney Joel Brodsky says they will continue to fight the use of hearsay evidence at the trial, itself.
Peterson, 58, is charged in the 2004 murder of his ex wife, Kathleen Savio. The former Bolingbrook police officer is also a suspect in the disappearance of his fourth wife, Stacy Peterson.
At issue: the use of statements Savio and Stacy said to others that prosecutors say are "critical" to their case -- and show motive. Peterson's defense attorneys have appealed the use of those previously excluded hearsay statements, but on Tuesday lawyers filed a motion to drop the fight in the appellate courts and move on with the trial. Peterson's attorneys have reportedly asked the Will County court to move forward as soon as possible.