This paper introduces a new domain for believable agents (BA) and presents novel methods for dealing with the unique challenges that arise therein. The domain is providing improvisational companionship to a specific musician/user, trading real-time solos with them in the jazz/blues setting. The ways in which this domain both conflicts with and benefits from traditional BA and interactive computer music system approaches are discussed. Band-out-of-the-Box (BoB), an agent built for this domain, is also presented, most novel in that unsupervised machine learning techniques are used to automatically configure BoB’s aesthetic musical sense to that of its specific user/musician.