A member of the Tadd Dameron Sextet, in his heyday he was in demand for his ability to play at the rapid tempos typical of bebop, and appears on several key recordings of the period. He left the music business in the late 1950s.
On May 1, 1951 Russell played in the recording session for Un Poco Loco, composed by American jazz pianist Bud Powell, with Max Roach on drums. Literary critic Harold Bloom included this performance on his short list of the greatest works of twentieth-century American art.
According to jazz historian Phil Schaap, the classic bebop tune “Donna Lee“, a contrafact on “Back Home Again in Indiana“, was named after Curley’s daughter. In 2002, she donated her father’s bass to the Institute of Jazz Studies at Rutgers University.