When musicians improvise together, they tend to agree beforehand on a common structure (e.g. a jazz standard) which helps them coordinate. However, in the particular case of collective free improvisation (CFI), musicians deliberately avoid having such a referent. How, then, can they coordinate? We propose that CFI musicians who have experience playing together come to share higher-level knowledge, which is not piece-specific but rather task-specific: an implicit mental model of what it is to improvise freely. We tested this hypothesis on a group of 19 expert improvisers from the Parisian CFI community, who had various degrees of experience playing with one another. Drawing from the methodology of team cognition, we used a card-sorting procedure on a set of 25 short improvised sound sequences to elicit and represent each participant’s mental model of the CFI task. We then evaluated the similarity between the participants’ models, and used the measure in a nearest neighbour classification algorithm to retrieve clusters of participants who were known to play together. As hypothesized, we found that the degree of similarity in participants’ mental models predicted their degree of musical familiarity with better-than-random accuracy: musicians who played together tended to ‘think’ about improvised music in the same way.