He performed a big-band arrangement of a medley from "West Side Story" that was released on the 1966 album "Swingin' New Big Band". The "West Side Story Medley", arranged by Bill Reddie, highlighted Rich's ability to blend his drumming into the band. Rich received the West Side Story arrangement of Leonard Bernstein's melodies from the musical in the mid-1960s; he found the music quite challenging and it took him almost a month of constant rehearsal to perfect. It later became a staple of his live performances. A six-minute performance of "Prologue/Jet Song" from the suite, performed during Frank Sinatra's portion of the Concert for the Americas on August 20, 1982, is on the DVD "Frank Sinatra: Concert for the Americas". In 2002, a DVD was released called "The Lost West Side Story Tapes" that captured a 1985 performance of this along with other numbers.