WASHINGTON - With the constitutionality of race-based affirmative action hanging by a thread at the Supreme Court, University of Texas officials are struggling to explain a policy that gives an extra edge to Latino and African American students from middle-class households and top-performing high schools.

It is called "qualitative diversity," and premier state universities, including the University of California, insist such policies are vital to preserving academic standards and combating stereotypes about minorities.

The case of Fisher v. University of Texas began six years ago when a rejected white student complained about the role race played in deciding who was admitted to the Austin campus.

Now, as the case returns for a second time to the high court, it has triggered a heated debate over who should benefit from affirmative action, what counts as diversity, and whether minority students from integrated suburban high schools may contribute more on campus than those from the inner city.

For about 80 percent of its admissions, the university currently operates under a race-neutral state law that awards admission to students who graduate in the top 7 percent of their high school class. (In an earlier version, it was the top 10 percent.)

The law has resulted in an influx of minority students to Austin, mainly from schools in low-income areas in the Rio Grande Valley and in the center cities of Houston, Dallas, and San Antonio.

But citing its interest in the "educational benefits of diversity," the university says it also needs to supplement that policy with a race-based one to admit promising minority students who are not in the top 7 percent of their class, including "the African-American or Hispanic child of successful professionals in Dallas." Critics say the policy is not only unfair to similar white students from the same schools, it effectively turns its back on the idea that affirmative action is intended to benefit disadvantaged students.

"Preferring minority students from wealthier, integrated backgrounds over minority students who have flourished despite economic hardships is at best counterintuitive, if not an outright distortion of the diversity rationale," said lawyers for Abigail Fisher, the white student who sued the university after she was denied admission in 2008.

Race-based admission policies have long drawn scrutiny from the Supreme Court, which will hear arguments in the case Dec. 9.

The court's conservatives say the guarantee of "equal protection" forbids universities from using race in deciding who is admitted.