Grönvall's musical career started in the 1980s group Sound of Music. The trio participated twice in the Swedish Eurovision Song Contest selections, Melodifestivalen, finishing fourth both times; in 1986 with "Eldorado" and in 1987 with "Alexandra". Over the following ten years, she established herself as a songwriter in Melodifestivalen, writing two songs for the 1992 competition and the 1995 runner-up "Det vackraste" ("The Most Beautiful Thing") performed by Cecilia Vennersten.

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From 1991 till 1997, she was one of the lead vocalists of the group One More Time with her husband Peter Grönvall and Maria Rådsten. They won the Melodifestivalen 1996 final with the folk-ballad "Den vilda" ("The Wilderness Mistress" engl version). It finished third (out of 23) in the Eurovision Song Contest 1996 behind Norway and winners Ireland.