AUSTIN, Texas — The House gave its final approval Tuesday to scaling back the law allowing automatic college admissions for high school students in the top 10 percent of their graduating class, a limit sought by the University of Texas at Austin.

Under the compromise bill, approved 123-20, the university could cap the number of Texas students admitted under the program to 75 percent of the entering resident freshman class. The bill would take effect in 2011, meaning it would cover students who are sophomores in high school this year.

"It's focused almost exclusively on UT-Austin," said Republican Rep. Dan Branch of Dallas, sponsor of the bill. Officials with the university have been pressing for such a change all session. They say they have lost control over who is admitted to the school because of the automatic admissions provided for in the existing law.

Most of the freshman class each year at the university is automatically occupied by students who graduated in the top 10 percent.

Differences will now have to be worked out between the House and Senate versions of the bill. The Senate provided for a cap at all state universities.

Two attempts by Rep. David Leibowitz, D-San Antonio, to amend the House bill Tuesday to hold down college tuition rates failed. One of his proposals would have frozen tuition for freshman at their first-year rate for four years, an idea Republican Gov. Rick Perry put forth a few months ago.

"It helps that student get out earlier, opens up a slot for another freshman," Leibowitz said. "We can bring in the next crop of freshmen."

The proposal approved in the House would expire after six years so the Legislature could judge the impact of the law and decide whether to continue it. It also would limit the number of nonresident students to 10 percent of the student body if the cap has taken effect.

The top 10 percent law was adopted a decade ago after a federal appeals court ruled affirmative action was illegal in Texas college admissions. In 2003, the U.S. Supreme Court allowed universities to use race as one of many decision-making factors.

A number of minority legislators and organizations say the top 10 percent law has improved racial and ethnic diversity at major universities.

Supporters of changing the law say it has caused a "brain drain" at UT-Austin, prompting exceptional students who fall just outside its top 10 percent parameters to go elsewhere, including out-of-state schools.

The top 10 percent cap bill is SB175.