He began his career working as the assistant to Joe Kubert in the "Tales of Green Berets" in 1965. His first titles for DC were "G.I. Combat" and "House of Mystery". During the 1970's he collaborated with Warner Brothers for Western Publishing comics. In the 1980's, Costanza worked with Marvel, drawing "Heathcliff", "Get-A-Long Gang", and "Hugga Bunch". He returned to Warner Brothers for the "Animaniacs" and "Looney Tunes" in the 1990's. Costanza has also done stories with Roger Rabbit and Mickey Mouse for Disney, and drawn comics with Matt Groening's "Simpsons". Most of Costanza's art work has been for funny animals but he primarily known as a letterer, notably having lettered hundreds of comics for DC Comics. He won the Shazam! Award in 1974 for best letterer. He served four years in the U.S. Air Force.