Cordileone is best-known for being traded in 1961 from the New York Giants to the San Francisco 49ers for quarterback Y. A. Tittle. At the time, Tittle was 34 years old and a 4-time Pro Bowler. Cordileone was quoted as reacting "Me, even up for Y. A. Tittle? You're kidding", and later remarked that the Giants traded him for "a 42-year-old quarterback".
His stay in San Francisco was short lived, as he went to the Rams in 1962, where he played only 2 games, before moving to Pittsburgh, playing 26 games until the end of the 1963 season. After a 3 year hiatus, he joined the expansion team New Orleans Saints for their first two seasons, 1967 and 1968, as offensive guard and defensive tackle. In his last season, he fumbled once, and returned an interception for 7 yards, after having recovered three fumbles in his first two pro seasons.