Thigpen first worked professionally in New York City with the Cootie Williams orchestra from 1951 to 1952 at the Savoy Ballroom. During this time he played with musicians such as Dinah Washington, Gil Mellé, Oscar Pettiford, Eddie Vinson, Paul Quinichette, Ernie Wilkins, Charlie Rouse, Lennie Tristano, Jutta Hipp, Johnny Hodges, Dorothy Ashby, Bud Powell, and Billy Taylor.
