We are currently witnessing a shift in the approach to combat traffic and consumption of illegal harmful drugs, being cannabis legalization a prominent example. In this paper, we study how to optimally regulate the market for cannabis, in a setting where consumers differ in their utility from consumption of the psychoactive component of cannabis, THC, and suffer from misperception of the health damage it causes. We analyze this problem through a vertical differentiation model, where a black market firm and a public firm compete in prices and qualities (THC content). A paternalistic government would like to correct for the misperceived health damage caused by cannabis consumption, as well as to reduce the size of the black market. It is the undesirability of black market profits what explains that the first-best allocation cannot be decentralized. We find two possible equilibria, depending on whether the public firm serves those consumers with the highest or lowest willingness to pay for quality. Paradoxically, when the public firm serves those consumers with higher taste for THC, a lower average health damage is achieved together with a better economic result for the public firm.