The case from New Haven, Conn., pits white firefighters, who showed up at the court Wednesday in their dress uniforms, against the city over its decision to scrap a promotion exam because no African-Americans and only two Hispanic firefighters were likely to be made lieutenants or captains based on the results.

As is often the case with closely fought social issues at the court, Justice Anthony Kennedy appeared to hold the key to the outcome. He seemed concerned that New Haven scuttled the test without determining that there were flaws that might have led to the racially disproportionate results.

"So shouldn't there be some standard that there has to be a significant, a strong showing after the test has been taken that it's deficient? Before it can be set aside?" he said.

Kennedy often frowns on racial classifications, yet he is not as opposed to drawing distinctions on the basis of race as his more conservative colleagues.

But where Kennedy saw shades of gray, the rest of the court seemed to view the case clearly in terms of black and white.

The court's 5-4 decision puts new limits on the ability of police to search a vehicle immediately after the arrest of a suspect.

Justice John Paul Stevens said in the majority opinion that warrantless searches still may be conducted if a car's passenger compartment is within reach of a suspect who has been removed from the vehicle or there is reason to believe evidence of a crime will be found.

"When these justifications are absent, a search of an arrestee's vehicle will be unreasonable unless police obtain a warrant," Stevens said.

Justice Samuel Alito, in dissent, complained that the decision upsets police practice that has developed since the court first authorized warrantless searches immediately following an arrest.

"There are cases in which it is unclear whether an arrestee could retrieve a weapon or evidence," Alito said.

The high court agreed to hear a U.S. Justice Department appeal defending the 1999 animal cruelty law after it was struck down for infringing free-speech protections.

A U.S. appeals court declared the law unconstitutional and overturned the conviction of a Virginia man, Robert Stevens, who sold three videos of pit bulls fighting each other and attacking hogs and wild boars.

His conviction in 2005 was the first in the country under the law. Stevens had been sentenced to 37 months in prison.

By a 10-3 vote, the appeals court rejected the government's argument that, for the first time in more than 25 years, there was a new category of speech not covered by constitutional free-speech protections. Usually, videos and other depictions are protected as free speech, even if they show abhorrent conduct.

Arizona state legislators and the state superintendent of public instruction want to be freed from federal court oversight of the state's programs for English learners. They've been ordered by a lower court judge to spend potentially hundreds of millions of dollars to comply with rulings in a 17-year-old case.

Parents of students attending southern Arizona's Nogales Unified School District sued the state in 1992, contending programs for English-language learners in Nogales were deficient and received inadequate funding from the state.

In 2000, a federal judge found that the state had violated the Equal Educational Opportunities Act's requirements for appropriate instruction for English-language learners. He ordered state legislators to create a plan to provide sufficient funds and placed the state's programs for non-English speaking students under court oversight.

Since then, the two sides have fought over what constitutes compliance with the order. Arizona has more than doubled the amount that schools receive per non-English speaking student and taken several other steps prescribed by the No Child Left Behind Act, a broader education accountability law passed by Congress in 2002.

Plaintiffs say that's not enough to comply with federal law and a judge agreed. But the state appealed, and now the high court will answer the question.