WASHINGTON - In historic arguments over voluntary school desegregation plans in Seattle and Louisville, Ky., a majority of the Supreme Court seemed skeptical Monday that race can be used even as a "tipping factor" in the decision to move students around to produce racially diverse schools.

But Justice Anthony Kennedy, probably the decisive vote, seemed to stop short of embracing assertions that the Constitution always requires colorblind approaches to school integration, such as magnet schools.

Either way, the court could effectively end voluntary integration plans in dozens of school districts. That would force administrators to find more subtle ways to ensure that children don't attend schools that reflect segregated housing patterns. Kennedy's distinctions might be the only hope for school districts that want to desegregate.

"When it came to the plans at issue, Kennedy certainly seemed to evince a good deal of hostility," said Ted Shaw, executive director of the NAACP Legal Defense and Education Fund, which is supporting the school districts.

"But I also think he was trying to figure out where the stopping point was or how far the argument ought to go," Shaw said. "I think he was looking for a limiting principle" for the idea of government colorblindness.

Kennedy was joined by Chief Justice John G. Roberts, Justice Antonin Scalia and Justice Samuel A. Alito Jr. in his criticism of the school plans. Justice Clarence Thomas, a longtime critic of race-conscious policies, typically doesn't speak during oral arguments but is widely expected to object to the plans.

The cases, Community Schools v. Seattle School District No. 1 and Meredith v. Jefferson County Board of Education, mark a return to the dicey question of how race fits into the Constitution.

The districts say integration is a key component of a public education, and is compelling enough to justify a limited use of race in policies designed to produce that integration.

Justice Stephen Breyer was particularly exercised over assertions that race-conscious integration efforts, which have been mandated by courts seeking to remedy past segregation, could be deemed unconstitutional.

"How could the Constitution, the day that that decree is removed, tell the school board it cannot make that effort anymore, it can't do what it's been doing, and we'll send the children back to their black schools and their white schools?" Breyer asked.