She excelled in portraying some of the more rarely heard and demanding dramatic soprano roles such as the woman in Schoenberg's Erwartung, Ursula in Hindemith's Mathis der Maler and Jenny in Weill's Rise and Fall of the City of Mahagonny.

[3] After finishing her studies, Nielsen made her professional opera debut as Laura in Millöcker's Der Bettelstudent at the Musiktheater im Revier in Gelsenkirchen in 1971.

She made her United States debut that year at the New York City Opera (NYCO) as Adele in Die Fledermaus by Johan Strauss.

The poor acoustics and the large size of the New York State Theater led Nielsen to try pushing her voice beyond her normal practice.

[3] Summer 1985 Nielsen recorded her first solo album with the Helsingborg Symphony Orchestra and Sir Antonio Pappano for Big Ben Phonogram.

Her first major critical success on the international stage was as Mozart's Konstanze at the Salzburg Festival (1987, 1989) and at the Royal Opera House (1988), both led by Sir Georg Solti.

[4] In her home country Nielsen was awarded the Tagea Brandt Rejselegat in 1984 and appointed Knight of Dannebrog by Queen Margrethe II of Denmark in 1992.

She taught as a guest professor at the Royal Academy of Music in Aarhus and gave masterclasses at numerous conservatories and institutions internationally.

Her farewell concert celebrating her 35 years in the profession took place in 2006 at the Tivoli Gardens but she was scheduled to return to the opera stage in early 2008 in Elektra by Richard Strauss in Venice and Die Frau ohne Schatten at the Deutsche Oper am Rhein at the time of her death.