Thursday is probably the Court's last session until October. The school rulings in cases affecting schools in Louisville, Ky., and Seattle leave public school systems with a limited arsenal to maintain racial diversity.

The court split, 5-4, with Chief Justice John Roberts announcing the court's judgment. Justice Stephen Breyer wrote a dissent that was joined by the court's other three liberals.

Justice Anthony Kennedy wrote a concurring opinion in which he said race may be a component of school district plans designed to achieve diversity.

He agreed with Roberts that the plans in Louisville and Seattle went too far. He said, however, that to the extent that Roberts' opinion could be interpreted as foreclosing the use of race in any circumstance, "I disagree with that reasoning."

The two school systems in Thursday's decisions employ slightly different methods of taking students' race into account when determining which school they would attend.

In the case involving the mentally ill killer in Texas, the court ruled 5-4 in the case of Scott Louis Panetti, who shot his in-laws to death 15 years ago in front of his wife and young daughter.

The convicted murderer says that he suffers from a severe documented illness that is the source of gross delusions. "This argument, we hold, should have been considered," said Justice Anthony Kennedy, who wrote the majority opinion.

Panetti's lawyers wanted the court to determine that people who cannot understand the connection between their crime and punishment because of mental illness may not be executed.

The Eighth Amendment of the Constitution bars "the execution of a person who is so lacking in rational understanding that he cannot comprehend that he is being put to death because of the crime he was convicted of committing," they said in court papers.

In a third case, the Court abandoned a 96-year-old ban on manufacturers and retailers setting price floors for products. In a 5-4 decision, the court said that agreements on minimum prices are legal if they promote competition.

The ruling means that accusations of minimum pricing pacts will be evaluated case by case. The Supreme Court declared in 1911 that minimum pricing agreements violate federal antitrust law.