With Stravinsky, he attended countless rehearsals, performances, and recording sessions of new Stravinsky works in such places as Boston, New York, and Venice (the first performance of The Rake's Progress in 1951). While teaching at Harvard Summer School in 1968, Spies conducted the first performances of four preliminary versions of Stravinsky's Les Noces along with a performance of the final version. At that session, he also conducted various works of Schoenberg and Anton Webern. Some of the musical comments shared between Spies and Stravinsky were reflected in articles written by Spies in several issues of Perspectives of New Music dealing with new works by Stravinsky.