There is evidence that music piracy has differential effects on artists depending on their popularity. We present a model of music piracy with endogenous copying costs: consumers’ costs of illegal downloads increase with the scarcity of a recording and are therefore negatively related to the number of originals sold. Allowing for a second source of revenues apart from record sales, we show that piracy can hurt some artists while benefiting others. Under plausible assumptions, piracy is beneficial to the most popular artists. However, this does not carry over to less popular artists, who are often harmed by piracy. We conclude that piracy tends to reduce musical variety.