New also imposed a gag order, barring the attorneys and relatives of the defendant and victim from talking with reporters until the trial is over.
Defense attorney Fortunato Perri successfully argued against allowing the three incidents into the trial, calling them remote.
Assistant District Attorney Michael Barry, however, said that allowing the jury to hear about the incidents would give jurors "the complete picture" about Tepper's off-duty penchant for drinking, escalating incidents, pulling a gun and blaming his victims.
Tepper, 45, spent 16 years on the police force before being fired and arrested in the fatal shooting of William Panas Jr., 21, on Nov. 21, 2009.
The shooting, in front of Tepper's Elkhart Street home, followed a fight involving Panas and another young man from the neighborhood.
At one point, according to 2010 preliminary-hearing testimony, Tepper pulled a gun, Panas dared him to shoot and Tepper fired once into the victim's chest.
Tepper had been attacked by Panas' friends and acted in self-defense, Perri has said.
Tepper is charged with murder, recklessly endangering another person and possession of an instrument of crime. He's been jailed without bail since being arrested Feb. 9, 2010.
The three gun incidents that New prohibited from being heard at trial occurred when Tepper was off duty and were investigated by the department's Internal Affairs Bureau, which cleared Tepper.
In 1995, he got into a car chase with two 21-year-old men who had said something inappropriate to Tepper's fiancee. He hit one of the men in the head with his gun and fist when he caught up to the car.
In 1996, he shot an opossum to death in the street in view of neighborhood children; and in 2002, he used pepper spray on a teenage boy and pulled a gun on a group of teens he accused of hanging his 8-year-old son from a fence by the back of the boy's pants.