We consider the optimal taxation of a good which exhibits a negative externality, in a setting where agents differ in their value for the good, their disutility for the externality and their value for money, and the planner observes neither. Pigouvian taxation is the unique Pareto efficient mechanism, but corresponds to the planner putting higher welfare weights on agents who are richer. We derive the optimal tax schedule for both a narrow allocative objective and a utilitarian objective for the planner. The optimal mechanism might take a “non-market” form and cap consumption, or forbid it altogether. The optimal mechanism is generically non-linear, and Pareto-inefficient.