Tully won the first two World Cup competitions, the 1977 and 1979 IAAF World Cup. He qualified for the 1980 U.S. Olympic team but was unable to compete due to the 1980 Summer Olympics boycott. Tully did however receive one of 461 Congressional Gold Medals created especially for the spurned athletes. He competed at the 1983 World Championships without registering a valid mark. In a one-month period in 1984 he raised the American record three times by a total of almost three inches. He concluded the season with a silver medal at the 1984 Olympic Games. He took the American record from Jeff Buckingham, but his national record was broken in 1985.