Alcohol consumption is associated with costs to society due to its impact on crime and health. Tax can lead consumers to internalise these externalities. We study optimal corrective taxation in the alcohol market. We allow for the fact that the externality generating commodity (ethanol) is available in many differentiated products, over which consumers might have heterogeneous preferences, and that there may also be heterogeneity in marginal externalities across consumers. We show that, if there is correlation in preferences and marginal externalities, setting different tax rates across products can improve welfare relative to a single tax rate on ethanol. We estimate a model of demand in the UK alcohol market and numerically solve for the optimal tax rates. Moving to an optimal system that taxes alcohol types at different rates would close half of the welfare gap between the current UK system and the first best.