We propose a model of the Music industry under piracy. We take into account quality, variety as well as price adjustments and show that our results fit quite well with empirical evidence. We then show that Peerto-Peer networks, and their corollaries that are free files-sharing, could have a positive impact on the Music Industry as a whole (recorded music, live music, and ancillary goods such as ringtones, etc.). However, given the present contractual arrangements that prevail in the music industry, record companies bear almost all of the negative impact of piracy whereas artists (as a whole) rather benefit from it. Royalties often amount for the smallest part of their income whereas piracy tends to boost live performances audience. Hence, rather to focus on deterring piracy by suing pirates, record companies should seek to extend their business frontiers, either by renegotiate music contracts with artists or, if it proves to be impossible, by a downstream vertical integration, especially towards the concert industry.