In his teen years, Cuccurullo became a devoted fan of Frank Zappa and began traveling to every show within 500 miles of his Brooklyn home. During the mid-1970s, he befriended several members of Zappa's band, including Terry Bozzio and Patrick O'Hearn. Over the next three years, he appeared with the band on stage at a couple of shows as well as in the 1979 Zappa film "Baby Snakes" (filmed October 1977). He impressed Frank Zappa by knowing the guitar parts to every Zappa song in the catalog, including the strangest sounds and most bizarre time signatures.