In 1962, he filed a suit on behalf of several African American residents of Little Rock to integrate the City’s public facilities including Robinson Auditorium. (The City Board and the Auditorium Commission were named in the lawsuit.) In 1963, the decision came down and the facilities had to integrate.
This lawsuit was just one of many in which Branton paved the way for equal opportunities for all. He helped desegregate the University of Arkansas School of Law and later filed suit against the Little Rock School Board in a case that went to the U.S. Supreme Court as Cooper v. Aaron.
A native of Pine Bluff, he graduated from what is now UAPB. After first being refused admission, he later became the fifth African American to attend the UA Law School and the third to graduate. From 1953 to 1962, he had a law practice in Pine Bluff. Between 1962 and 1965, Branton worked with representatives of the major African-American civil rights organizations to register almost 700,000 new black voters in eleven Southern states. Following that, he became executive director of the President’s Council on Equal Opportunity and help coordinate implementation of the Civil Rights Act of 1964. He spent 1965 to 1967 at the Justice Department, before becoming executive director of the United Planning Organization (UPO). After working with a couple of other organizations, he returned to private practice in 1971. In December 1977 it was announced that Branton would be the new dean of Howard University School of Law. After five years, he joined the law firm of Sidley and Austin in its Washington DC office.
Branton died of a heart attack in December 1988. Eleven hundred mourners gathered at a memorial service at the Washington National Cathedral in Washington, D.C. Among those present was Supreme Court Justice Thurgood Marshall. The eulogy was delivered by Vernon E. Jordan, Jr.. Then-Gov. Bill Clinton spoke at the Pine Bluff memorial service for Branton.