The next Olympic Games were held in 1996 in Atlanta. She finished sixth in 400 m hurdles, as the best European athlete. Unlike the 1993 Universiade, she finished 0.06 seconds behind fourth-placed Debbie-Ann Parris. The medalists ran in the range of 52.8-53.2 seconds, whereas Meissner ran in a career best time of 54.03 seconds. This result ranks her fourth among German 400 m hurdlers through all time, behind Sabine Busch, Cornelia Ullrich and Ellen Fiedler. Her success continued at the 1997 World Indoor Championships, where she won a bronze medal in the relay, this time with Anja Rücker, Anke Feller and Grit Breuer. Meißner ran the third leg. She did not compete in any individual distance as the 400 metres hurdles is not contested during the indoor season.