Group musical improvisation is a unique psychological phenomenon. Cognitive literature on jazz musicians argues that creativity in improvisation is constrained by stylistic conventions and facility with existing musical elements. However the expanding field of free improvisation is predicated on avoiding idiomatic expectations and familiar material. To model musical improvisation in its widest sense, 15 diverse free improvisers were video recorded performing in trios, and interviewed in-depth while reviewing the recording. Improvisers chose on an iterative basis whether to maintain what they were doing or change, either to initiate a new direction or to respond to another improviser. Responses were subjectively understood to adopt, augment or contrast the contributions of others. These choices were based on evaluative dimensions of texture, rate of initiatives, and degrees of novelty and diversity, as well as structural and practical concerns and experience of enjoyment. Improvisers did not perceive consistent agency for themselves while improvising, and their evaluations were influenced by constructions of the social context. Results highlight that new material is generated at a variable rate by any one individual during this collaborative creativity, and indicate that constraints on choices to cope with high cognitive demands are subjective and situation-specific rather than objective.