Digital piracy, although negatively altering the recorded music market, has a positive impact on other segments of the music market, such as live music or ancillary goods, because it generates a positive externality benefiting those activities. Through a 2-player strategic game between a record company and an artist, this study shows that a renegotiation of music contracts could allow the internalizing of this positive externality, while being welfare-improving for both record companies and artists. This study also shows, however, that pervasive piracy is not desirable for an artist.