Trumpet player Chet Baker (1929-1988) started manifesting himself as a singer in the 1950s. Because of drug abuse and dental problems his qualities slowly declined. Still, his singing and recitation kept a certain charm, as you can hear in this recording from 1985 and 1986.
Sources:
Chet Baker: As Time Goes By (Timeless CD)
idem: Chet Baker Sings Again (Timeless CD)