- 2007 - Pulitzer Prize for Music in Music Nomination: Grendel (Opera)
- 2004 - Emmy Awards Nomination, "Great Performances: Dance in America" - Outstanding Music Composition for a Miniseries, Movie or a Special
- 2002 - Academy Awards, Best Original Score: Frida
- 2002 - Academy Awards (Nominee), Best Original Song: Frida, "Burn It Blue"
- 2002 - Golden Globes, Best Original Score: Frida
- 1999 - CFCA Awards (Nominee), Best Original Score: The Butcher Boy
- 1998 - Chicago Film Critics Awards (Nominee), Best Original Score: The Butcher Boy
- 1998 - Los Angeles FCA Awards (Win), Best Original Score: The Butcher Boy
- 1997 - Tony Awards (Nominee), Best Original Musical Score: Juan Darien: A Carnival Mass
- 1997 - Grammy Nomination: A Time to Kill, "Defile and Lament"
- 1996 - Academy Awards (Nominee), Best Original Score: Michael Collins
- 1996 - Golden Globe (Nominee), Best Original Score: Michael Collins
- 1995 - Grammys (Nominee), Best Instrumental Composition: Batman Forever
- 1995 - Golden Globe (Nominee), Best Original Score: Interview with the Vampire
- 1994 - Academy Awards (Nominee), Best Original Score: Interview with the Vampire
- 1990 - Edinburgh Festival Critics Choice Award, Best Music: Juan Darien: A Carnival Mass
- 1990 - American Academy of Arts and Letters Richard Rodgers Award Win, Best Music: Juan Darien: A Carnival Mass
- 1988 - Obie Award, Best Music: Juan Darien: A Carnival Mass
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