This paper is centred around the analysis of the creative process underlying the genesis of a recent work of music by French composer Karl Naëgelen, Fenêtre Ovale (2011), written in collaboration with two free improvisers active on the Parisian scene, Ève Risser (piano) and Joris Rühl (clarinet). This piece is remarkable in that, contrary to the vast majority of works composed in a so-called “comprovisation” framework, where the interaction between the composed and the improvised elements essentially takes place during the moments of performance, its score never actually requires any act of improvisation from its performers: the relation between improvisation and composition is thus entirely implicit, underlying the creative process itself rather than its product. Using the work’s various sketches, and the numerous improvisations realized by the two musicians over the course of the composition of Fenêtre Ovale, I show that improvisation played three distinct roles in the creative process: 1. A role of stimulation: the improvisation enables the generation of new compositional ideas; 2. An inspirational role: the ideas generated by improvisation are transferred, more or less directly, in the compositional setting; 3. A role of simulation: the improvisation is used to simulate a certain musical organization and/or to validate or invalidate a given compositional choice. But improvisation is also embedded in the compositional project itself at a deeper level: improvisation is indeed used as a model for the composition, which seeks to emulate some of its most notable aesthetic properties. This is mainly done by importing into the score some of the specific instrumental and musical gestures used by the musicians in an improvisational setting. However, this attempt to absorb improvisational gestures into composition is not straightforward: it reveals some of the fundamental differences existing between the compositional gesture and the improviser's gestures. The paper thus concludes by discussing the intrinsic paradoxes and tensions that lie at the heart of such a project.