Dragieva made her international debut at a major tournament at the 1987 European Athletics Indoor Championships and she placed seventh with her best jump of . She reached the peak of her career shortly after at the 1987 IAAF World Indoor Championships. She cleared in the final to take the bronze medal behind fellow Bulgarian Kostadinova and Germany's Susanne Beyer. This performance ranked her third in the world indoors that year. Her jump was also the best ever indoors by a European under-23 athlete. This record lasted until 2002, when Marina Kuptsova improved it by three centimetres.