Discographie :
1977 : My Aim Is True
1978 : This Year's Model
1978 : Live at the El Mocambo
1979 : Armed Forces
1980 : Get Happy!!
1981 : Trust
1981 : Almost Blue
1982 : Imperial Bedroom
1983 : Punch the Clock
1984 : Goodbye Cruel World
1986 : King of America
1986 : Blood and Chocolate
1989 : Spike
1991 : Mighty Like a Rose
1991 : G.B.H.
1993 : The Juliet Letters
1994 : Brutal Youth
1995 : Kojak Variety
1995 : Deep Dead Blue
1995 : Jake's Progress
1996 : All This Useless Beauty
1996 : Costello & Nieve
1997 : Terror & Magnificence
1998 : Painted from Memory
1999 : The Sweetest Punch
2001 : For the Stars
2002 : When I Was Cruel
2002 : Cruel Smile
2003 : North
2004 : The Delivery Man
2004 : Il Sogno
2005 : Piano Jazz: McPartland/Costello
2006 : My Flame Burns Blue
2006 : The River in Reverse
2008 : Momofuku