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Haymer played alto saxophone from age 15 and picked up tenor at age 20. He played with the Carl Sears-Johnny Watson Band, then played with Rudy Vallee, Charlie Barnet, Red Norvo (1935–1937), Jimmy Dorsey (1937–1941), Woody Herman (1941–1942), Kay Kyser (1942–1943), Benny Goodman (1943) and Dave Hudkins (1944). In 1944 he enlisted in the Navy, and after returning in 1945 he worked as a session musician in Los Angeles, in addition to dates with Red Nichols and Goodman. In 1945 he led a quintet featuring Charlie Shavers and Nat King Cole on recording, and had three songs issued on Keynote Records in 1946. In 1949 he recorded with Frank Sinatra and was killed in an automobile accident after a session.