With Paul Vance he co-wrote "Itsy Bitsy Teenie Weenie Yellow Polka Dot Bikini", recorded in 1960 by Brian Hyland; the Grammy-nominated "Catch a Falling Star", recorded in 1957 by Perry Como; and the 1969 hit, "Tracy", recorded by The Cuff Links.
With lyricist Anne Croswell he wrote the songs for the Broadway musical Tovarich starring Vivien Leigh, which received a Grammy nomination for Original Cast Album. Pockriss and Croswell have also collaborated on the frequently produced Ernest in Love (based on The Importance of Being Earnest) and Bodo. Pockriss also wrote the music for the musicals Wonderful Olly, Dolley Madison, and Divorce Of Course.
Pockriss wrote seven original songs for MGM's full length animated film The Phantom Tollbooth, scored the film The Subject Was Roses and wrote the title songs for One, Two, Three and the Western classic, Stagecoach.