Boston has several elite high schools where admission is determined by test scores. The most famous is the Boston Latin School. The Boston school board debated the admissions policy at length and voted unanimously to change it, to open the way for less advantaged students.

The Boston School Committee on Wednesday night unanimously approved the biggest overhaul of the city’s exam school admission process in more than two decades, adopting a new system that should give disadvantaged students a better chance of getting in…

The effort to change the admission requirements had generated heated debate among parents and a backlash over last-minute political meddling that initially influenced the proposal presented to the School Committee two weeks ago.

Hours before the meeting started Wednesday, Superintendent Brenda Cassellius stepped into the fray, releasing final recommendations that rejected a politically influenced measure reluctantly advanced by a task force that would have reserved 20 percent of all seats to students with the highest ranking composite scores citywide. The remainder would have been allocated in rank order within tiers based on geography and socioeconomic factors.

Instead, Cassellius favored the task force’s original desire to allocate all seats for Boston Latin School, Boston Latin Academy, and the O’Bryant School of Math and Science through eight tiers based on census tracts. The approach would group together qualified applicants from areas of the city with similar socioeconomic characteristics in an effort to reduce the likelihood that a low-income applicant would compete against an affluent one.

The task force abruptly abandoned the measure at their final meeting two weeks ago after its cochairs warned that they were under political pressure to create the 20 percent set-aside for students with the highest composite scores citywide and that the consequences of not doing so could be severe for the school system.

The political interference created a backlash among many parents and advocates who pushed to get rid of the 20 percent set-aside, while other parents advocated for a citywide competition for all seats. Cassellius said the backlash factored into her decision to drop the set-aside in an effort to restore public trust in the process.

”What is being considered tonight, I believe to be a huge step forward for our students, especially our students who have not been able to access our exam schools through no fault of their own,” Cassellius told the School Committee as she introduced the final recommendations. “While some of us might wish for a sweeping mandate that would dismantle, you know, ages of privilege and create equitable opportunity with one vote of the School Committee . . . I also know that holding out for a perfect solution could possibly lose this moment.”

The new admission policy replaces a far simpler process that has been used for more than two decades and allocated seats to applicants citywide in rank order based on an equal weighting of their grades and entrance exam scores.

Under the new policy, grades will carry greater weight, comprising 70 percent of the composite score for admission and an entrance exam will make up 30 percent. The entrance exam will be suspended again this fall for those seeking admission for fall 2022 due to disruptions caused by the pandemic, and only this upcoming school year’s grades will be used.