A judge ruled that George Zimmerman, who's charged with murder in the death of Trayvon Martin, must remain on GPS monitoring and cannot leave Seminole County.

Judge Debra Nelson heard several motions in the case on Tuesday, and Zimmerman appeared at the hearing wearing a suit coat and tie while sitting next to his lead attorney, Mark O'Mara.

Besides dropping the monitoring, the defense wanted Zimmerman to be able to live outside Seminole County.

O'Mara said it's been frustrating for Zimmerman not to be able to leave the county as part of his bond condition.  O'Mara said Zimmerman was not a threat to flee, and a probation officer testified that he's not had any problems with Zimmerman.

The state, however, reminded Nelson that Zimmerman previously lied to the court -- when another judge was overseeing the case -- about his ability to post bond.

Zimmerman's attorneys also sought copies of FBI communications with investigators.

The next hearing in the case is set for early January.

Zimmerman is charged with second-degree murder in the shooting of 17-year-old Martin following an altercation in Sanford in February.

He has pleaded not guilty, claiming self-defense under Florida's "stand your ground" law.

Last week, the state released more information in the case, including a photo showing Zimmerman with a bloody, swollen nose.

Nelson has set a trial date for June 10 and a "stand your ground" hearing for 45 days before trial.

Zimmerman's family speaks

Zimmerman's family recently spoke up for the first time, appearing on the Spanish-language network Univision's "Al Punto with Jorge Ramos." While his mother's face could not be seen during the interview, she talked about a wide-range of topics, including the allegations that race played a role in the shooting death.

"My son defended his own life. The young man who attacked him for whatever reason that we don't know has left a print and thank God there is a picture to prove that," his mother Gladys Zimmerman said in Spanish.

Defense attorneys released a color photograph earlier this month of a swollen and bruised Zimmerman with blood dripping from his mouth. It had previously been released in only black and white forms.

Zimmerman's mother told Ramos the picture and 911 calls prove her son was fearing for his life when he shot Martin.

"The only thing that I'm going to tell you is put my son's picture like that in color and put the tape in which he asks for help, help in which many say is in my son's voice."

Zimmerman's brother, Robert, also sat down for the interview. He weighed in on the lawsuit filed against NBC for the way the network edited a call to police after the shooting. In it, Zimmerman is heard saying Martin was black, but only after being asked by a 911 operator.