Researchers wishing to create computational systems that themselves generate artworks face two interacting challenges. The first is that the standards by which artistic output is judged are notoriously difficult to quantify. The larger AI community is currently involved in a rich internal dialogue on methodological issues, standards, and rigor, and hence murkiness with regard to the assessment of output must be faced squarely. The second challenge is that any artwork exists within an extraordinarily rich cultural and historical context, and it is rare that an artist who is ignorant of this context will produce acceptable works. In this paper we assert that these considerations argue for case-based AI/Art systems that take critical criteria as parameters. We describe an example system that produces new bebop jazz melodies from a case-base of melodies, using genetic programming techniques and a fitness function based on user-provided critical criteria. We discuss the role that such techniques may play in future work on AI and the arts.