We explore the effects of environmental taxes that imprecisely target pollution. A review of actual policies indicates few (if any) examples of a true tax on pollution. More typically, environmental taxes target an input or output that is correlated with pollution. We construct a simple analytical general equilibrium model to calculate the optimum tax rate on the output of the polluting industry, in terms of key behavioural parameters, and we compare this imprecisely-targeted tax to an ideal tax on pollution. Finally, we consider incremental tax reforms such as a change in either tax from some pre-existing level. Using a utility-based money-metric measure of welfare, we examine the losses that arise from not taxing pollution directly. With no existing tax, under our plausible parameters, the welfare gain from an output tax is less than half the gain from an emissions tax.