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Bovenberg and de Mooij (1994) showed that, in the presence of preexisting distorting taxes, the optimal pollution tax typically lies below social marginal damages. The authors view this result as a refutation of the so-called "double dividend hypothesis," which suggests that a tax on pollution can both improve the environment and reduce distortions in the tax system. Their paper spawned a large literature on optimal environmental tax rates in a second-best world. In this note, I argue that the emphasis on tax rates is misguided. Using an analytical general equilibrium model, I show that for reasonable parameter values, an increase in tax distortions (arising from an increase in required tax revenues) leads to a fall in the optimal Pigouvian tax while environmental quality improves. In general, knowledge of the direction of changes in optimal environmental tax rates due to changes in the economy is not sufficient for understanding the impact on environmental quality.