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In a ruling that avoided some difficult constitutional issues, the justices said a court may approve the use of race as a factor in admissions -- but only after it concludes that "no workable race-neutral alternatives would produce the educational benefits of diversity."

The decision didn't question the underpinnings of affirmative action, which the court last reaffirmed a decade ago.

The high court ordered the federal appeals court in New Orleans to take another look at the case of Abigail Fisher. She's a white Texan who wasn't offered a spot at the University of Texas in Austin in 2008. She has since received a degree from Louisiana State.

The justices said the appeals court didn't apply the highest level of judicial scrutiny when it upheld a Texas plan that uses race as one among many factors in admitting about a quarter of the university's incoming freshmen. The school gives the bulk of the slots to Texans who are admitted based on their high school class rank, without regard to race.