Jury selection will begin June 10 in the trial of George Zimmerman, the Florida man accused of second-degree murder in the February 2012 death of African-American teenager Trayvon Martin.

Tuesday morning in Sanford, Fla., a judge ruled that both prosecutors and Zimmerman's defense team have had ample time to prepare their cases, NPR's Greg Allen tells our Newscast Desk. She turned down a request from Zimmerman's attorney for more time.

The judge also, as The Orlando Sentinel reports, "ruled for the state on several key issues: The defense may not bring up Trayvon Martin's past marijuana use at trial, or his school suspensions or alleged participation in fights, without clearing several legal hurdles and another ruling granting permission."

Prosecutors say Zimmerman, a self-appointed neighborhood watch volunteer, shot and killed 17-year-old Trayvon after calling police to say that a "suspicious" young man was walking through his Sanford neighborhood.

The killing drew national attention after Trayvon's family and its supporters said authorities had not moved quickly to investigate the killing or to challenge Zimmerman's claim that he acted in self defense. They alleged that Zimmerman had racially profiled Trayvon. There were rallies in many major cities. After the appointment of a new prosecutor to the case, Zimmerman was arrested on April 11. He has pleaded not guilty, saying that Trayvon attacked him.

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