The band consisted of Gösta Sundqvist, Risto Paananen, Juha Karastie and Niklas Nylund.
Sundqvist's lyrics often deal with the humiliated aspirations and crushed hopes of average people, as in the song "Teuvo, maanteiden kuningas" ("Teuvo, king of the highways"), which tells the story of a reckless boy with dreams of becoming a rally champion, or "Pimeä Tie, Mukavaa Matkaa" ("Dark Road, Farewell") which describes the final moments of a family preparing to commit vehicular suicide after they were unable to afford a place to live.
Sexual themes, considered from somewhat unconventional points of view, feature in many Leevi hits such as "Sopivasti lihava" ("Suitably Fat"), "Kyllikki" and "Unelmia ja toimistohommia" ("Dreams and office work").
The instrumental "Tuhannen markan seteli" ("Thousand Mark Note") from the album "Suuteleminen kielletty" was for many years the theme song of "Urheiluruutu", a major sporting news program, on Finnish television.
On August 15, 2003, Sundqvist died of a sudden heart attack at the age of 46, and the band decided to break up.