Konrad "Conny" Bauer is a German free jazz trombonist. He is the brother of the trombonist Johannes Bauer.

Free jazz or Free Form in the early- to mid-1970s is a style of avant-garde jazz or an experimental approach to jazz improvisation that developed in the late 1950s and early 1960s when musicians attempted to change or break down jazz conventions, such as regular tempos, tones, and chord changes. Musicians during this period believed that the bebop and modal jazz that had been played before them was too limiting, and became preoccupied with creating something new. The term "free jazz" was drawn from the 1960 Ornette Coleman recording Free Jazz: A Collective Improvisation. Europeans tend to favor the term "free improvisation". Others have used "modern jazz", "creative music", and "art music".