After Caspi's military service, "The Three Fat Men" became the "They Don't Care" trio. In the Yom Kippur War he toured army bases along with Leonard Cohen, who arranged his 1974 song "Lover Lover Lover" with Caspi. During the 70s he worked closely with Ehud Manor, another Israeli songwriter, and released some of his most popular songs: "Lo Yadati SheTelchi Mimeni" (I Didn’t Know You Would Leave Me), "Brit Olam" (Covenant of Love), and "Shir HaYonah" (The Song of the Dove).