In August 1980, Conz ran her first international race and won second place at the Avon International Marathon for Women in London, England. Conz wore bib number 184. Conz finished in 2:36:02, and it was also the #2 time in the world that year. She returned the following year to win Avon, this time in Ottawa, beating her friend and future; winning the first ever women's Olympic gold medalist in the marathon, Joan Benoit. She also won Freihofer's Run for Women that same year. In 1982, she won the Chicago Marathon in a personal best of 2:33:22.