Vukcevich continued to play chess. In 1969 he was joint winner of the U.S. Open Chess Championship, along with Pal Benko and Robert Byrne. In 1975 he finished third in the U.S. Championship, ahead of Samuel Reshevsky, Robert Byrne, Larry Evans and Arthur Bisguier among others. From 1976-79, he played in the National Telephone League, scoring 16.5 from 22 games, including wins against Bisguier, Yasser Seirawan, Nick De Firmian and Leonid Shamkovich.
