Alcohol 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 market. We find that heavy drinkers have systematically different patterns of alcohol demands and welfare gains from optimally varying rates are higher the more concentrated externalities are among heavy drinkers.