We study optimal corrective taxation in the alcohol market. Consumption generates negative externalities that are non-linear in the total amount of alcohol consumed. If tastes for products are heterogeneous and correlated with marginal externalities, then varying tax rates on different products can lead to welfare gains. We study this problem in an optimal tax framework and empirically for the UK alcohol market. Welfare gains from optimally varying rates are higher the more concentrated externalities are amongst heavy drinkers. A sufficient statistics approach is informative about the direction of reform, but not about optimal rates when externalities are highly concentrated.