A narrowly divided Supreme Court on Thursday upheld the race-conscious admissions policy at the University of Texas (UT), handing diversity advocates a surprise win before the Court.

Justice Anthony Kennedy delivered the 4-3 decision in Fisher v. University of Texas for the Roberts Court. Joined by Justices Ruth Bader Ginsburg, Stephen Breyer, and Sonia Sotomayor, the majority held that the university program does not violate the Constitution’s guarantee of equal protection of the laws.

Justice Elena Kagan had recused herself for prior work on the case in the U.S. Solicitor General’s office.

The case concerned the University of Texas’ admissions program, which has been the target of anti-affirmative action advocates for years. The program guarantees acceptance to the top 10 percent of students in every high school in the state.

But the admissions program has a second component: Remaining applicants from Texas and elsewhere are considered under standards that take into account various factors, including academic achievement, race, and ethnicity. It was that second component being challenged before the Court.

Abigail Fisher, a white woman, first challenged the policy in 2008, claiming the university had denied her admission based on her race. Fisher did not meet the top 10 percent threshold to get into the University of Texas at Austin, so her application was considered and rejected by administrators under the second portion of the university’s admissions policy. That challenge landed before the Roberts Court in 2013. But instead of deciding then whether or not UT’s policy was constitutional, the Roberts Court sent the case back to the lower courts for reconsideration. The Fifth Circuit ruled in favor of UT’s policy, and Fisher appealed to the Supreme Court again.

Thursday’s decision affirms that lower court decision upholding the university’s policy.

“A university is in large part defined by those intangible ‘qualities which are incapable of objective measurement but which make for greatness,’” Justice Kennedy wrote, quoting from key civil rights case Sweatt v. Painter. “Considerable deference is owed to a university in defining those intangible characteristics, like student body diversity, that are central to its identity and educational mission.”

But while a win for diversity advocates, the decision signaled a compromise as Kennedy suggested considering race and ethnicity in admissions policies is something that should be “ongoing” and “subject to refinement.”

“The Court’s affirmance of the University’s admissions policy today does not necessarily mean the University may rely on that same policy without refinement,” Kennedy wrote. “It is the University’s ongoing obligation to engage in constant deliberation and continued reflection regarding its admissions policies.”

Edward Blum, president of the Project on Fair Representation, a conservative legal organization that opposes “racial preferences” in government, organized and funded Fisher’s challenge. Blum’s organization also brought the legal challenge that resulted in the justices striking a key provision of the Voting Rights Act in 2013.

Fisher issued a statement shortly after the decision: “I am disappointed that the Supreme Court has ruled that students applying to the Univ. of Texas can be treated differently because of their race or ethnicity. I hope that the nation will one day move beyond affirmative action.”