Alexander's scores included several Mickey Rooney films, such as The Atomic Kid (1954), The Twinkle in God's Eye (1955), Baby Face Nelson (1957), The Last Mile (1959), The Big Operator (1959) and The Private Lives of Adam and Eve (1960), as well as the scores to 13 Frightened Girls (1963), Strait-Jacket (1964), I Saw What You Did (1965) and Tarzan and the Valley of Gold (1966).

He provided music for the television shows Hazel, The Farmer's Daughter, Bewitched, I Dream of Jeannie, Dennis the Menace and The Wacky World of Jonathan Winters.

He arranged and conducted for variety shows starring Dean Martin, Gordon MacRae, Mickey Rooney, and James Stewart.

He was involved in recording sessions with Doris Day, Benny Goodman, Peggy Lee, Dinah Shore, Kay Starr, Dakota Staton, and Paul Whiteman.

[7] He is buried in the Sanctuary of Meditation mausoleum, row 1, space 15a, in Hillside Memorial Park, Los Angeles, California.