Randy Newman limps across the blue carpeting of his home studio, past the grand piano and a window looking onto a stream running through his back yard, and pauses at a cluttered countertop, his eyes settling on a piece of sheet music. "This is a song I had to write for a goddamn alligator," Newman says.

In the early Seventies, Newman released three of the darkest, wittiest albums of the decade: 12 Songs, Sail Away...

Newman works with piano, an orchestra and a Dixieland-style combo, using...