Miloșovici won the bronze medal on floor at the 1996 World Championships, before winning the team and floor gold medals at the European Championships. She also finished third in the all around. Miloșovici led the Romanian team to a bronze at the 1996 Olympics, in spite of a spate of injuries that left the squad depleted of several key gymnasts and forced them to compete with only six athletes instead of seven. Milosovici had the rare opportunity to improve upon her third place all around finish in Barcelona; with her consistency and competitors' mistakes, she was tied for the bronze with Amanar, and became the first gymnast since Nadia Comăneci to medal in the all around at consecutive Olympics. This also marked her fourth all-around medal in World and Olympic competition, a feat since equalled only by Svetlana Khorkina, Aliya Mustafina and Simone Biles. In her final competition, she finished eighth in the uneven bars final. She originally qualified for the beam final, but was replaced by her teammate Alexandra Marinescu.