Austin, Tex. — The Texas Senate voted today to limit a controversial policy that requires public universities to admit Texas students who graduate in the top 10 percent of their high-school classes.

The bill, which is scheduled for a final Senate vote on Wednesday before moving on to the State House of Representatives, would allow universities to cap the number of students admitted under the policy at 60 percent of their freshman class. According to reports in the Austin American-Statesman and The Dallas Morning News, “top 10-percenters” filled 81 percent of the freshman seats at the University of Texas’ flagship campus at Austin this year, and officials said that proportion could rise to 86 percent next year and 100 percent within four years.

University leaders have appealed for more flexibility to accept other promising students, such as those who have academic, artistic, or leadership abilities but who don’t fall into the top tier for automatic admission. Opponents have warned that relaxing the automatic-admission policy would hurt efforts to enroll more minority students, but the bill’s author, Sen. Florence Shapiro, a Republican from Plano, said lawmakers would take corrective action if that happened.

In 2007 the Senate passed a similar measure restricting the automatic-admission policy, but it was voted down by the House.

Today’s bill passed by a vote of 22 to 8 after a sweetener was thrown in for low-income students who fall into the top 10 percent, but might not qualify for automatic admission to the campus of their choice under the revised plan. The amendment stipulates that all low-income students graduating in the top 10 percent of their high-school classes would receive full scholarships to attend a public university.

Under another amendment, the limitations on the top-10-percent law would expire after eight years unless the Legislature extended them. —Katherine Mangan