Spector's first trial ended in September with a deadlocked jury. Spector, famed for his revolutionary "Wall of Sound" recording technique, is accused of killing actress Lana Clarkson at his Alhambra mansion on Feb. 3, 2003.
Fidler set a trial date of Sept. 29, and also set a hearing on motions for July 29.
Spector's lawyer, Doron Weinberg, said it would be a week or two before the Supreme Court makes a decision.
Clarkson, 40, best known for her role in the cult film "Barbarian Queen," was working as a hostess at the House of Blues when she met Spector and went home with him.
Spector, 69, attended Thursday's hearing with his wife, Rachelle. He was decked out in one of his signature frock-coat suits and wearing a large button on his lapel that read "Obama Rocks."
Clarkson's mother, sister and a family lawyer sat in the front row of the courtroom. They are waiting for resolution of the criminal case before they pursue a wrongful-death lawsuit against Spector.
In its Supreme Court brief, the defense argued that Fidler's rulings toward the end of the first trial were designed to ensure Spector's conviction, in part to counter media reports that a celebrity could not be convicted in a Los Angeles court. Fidler has denied that and turned down a bid to remove himself from the second trial.
The district attorney's office has argued that Fidler was "scrupulously fair to the defendant."