We study the introduction of a price floor for alcohol that is aimed at correcting for negative consumption externalities. Policy effectiveness depends on whether the measure achieves large reductions in the most socially costly consumption. We exploit a natural experiment to show the policy raised prices of cheap products favored by heavy consumers, and achieved large demand reductions among this group. We use pre-reform data to estimate a model of consumer demand that is able to match these patterns, and use this to compare the welfare performance of a price floor with the counterfactual introduction of an ethanol tax. We show that if the marginal external cost of drinking is at least moderately higher for heavy drinkers, then a price floor is better targeted at the most socially costly consumption and therefore achieves larger welfare gains than an ethanol tax. Although the price floor leads to a larger fraction of the consumer burden falling on those with low incomes compared with the tax reform, it leads to a consumer burden that is smaller for all income groups.