The Supreme Court said Monday it will dive back into the fight over the use of race in admissions at the University of Texas, a decision that presages tighter limits on affirmative action in higher education.

The justices said they will hear for a second time the case of a white woman who was denied admission to the university's flagship Austin campus.

The conservative-leaning federal appeals court in New Orleans has twice upheld the university's admissions process, including in a ruling last year that followed a Supreme Court order to reconsider the woman's case.

The case began in 2008 when Abigail Fisher, who is white, was denied admission to the University of Texas's flagship Austin campus because she did not graduate in the top 10 percent of her high school class — the criterion for 75 percent of the school's admissions. The university also passed her over for a position among the remaining 25 percent, which is reserved for special scholarships and people who meet a formula for personal achievement that includes race as a factor.

The case went to the U.S. Supreme Court in June 2013. But rather than issue a landmark decision on affirmative action, it voted 7-1 to tell a lower appeals court to take another look at Fisher's lawsuit. That meant the university's admissions policies remained unchanged.

Last year, the 5th U.S. Circuit Court of Appeals again upheld the university's admissions policy. Fisher is a graduate of Louisiana State University.

Justice Elena Kagan is not taking part in the case. She sat out the first round as well, presumably because of her work on the case when she served in the Justice Department before joining the court.