Awards
- 1981 Grammy Award (Best Jazz Instrumental Performance by a Big Band) for Walk on the Water
- Grammy nominations for the albums The Age of Steam, For an Unfinished Woman and Soft Lights and Sweet Music
- 1982 The Birth of the Cool album inducted into the Grammy Hall of Fame
- 1982 Connecticut Arts Award
- 1984 Viotti Prize (Vercelli, Italy)
- 1984 inducted into the Big Band and Jazz Hall of Fame
- 1988 Duke Ellington Fellow at Yale University
- 1989 received keys to the city of Trieste, Italy
- 1990 Philadelphia Music Foundation Hall of Fame
- 1991 American Jazz Hall of Fame
- 1992 Lionel Hampton School of Music Hall of Fame
- 1992 Guest composer at the Mertens Contemporary American Composer's Festival, University of Bridgeport, Connecticut
- 1994 Down Beat Jazz Hall of Fame
- 1995 Artists Committee for the Kennedy Center Honors for the Performing Arts
- 42 consecutive years (1953–1995) winning the Down Beat magazine reader's poll for outstanding baritone saxophonist
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