For political, jurisdictional and technical reasons, environmental regulation of industrial pollution is often incomplete: regulations apply to only a subset of facilities contributing to a pollution problem. Policymakers are increasingly concerned about the emissions leakage that may occur if unregulated production can be easily substituted for production at regulated firms. This paper analyzes emissions leakage in an incompletely regulated and imperfectly competitive industry. When regulated producers are less polluting than their unregulated ounterparts, emissions under incomplete regulation can exceed the level of emissions that would have occurred in the absence of regulation. Converseley, when regulated firms are relatively more polluting, aggregate emissions under complete regulation can exceed aggregate emissions under incomplete regulation. In a straightforward application of the theory of the second best, I show that incomplete regulation can welfare dominate complete regulation of emissions from an asymmetric oligopoly. The model is used to simulate greenhouse gas emissions from California's electricity sector under a source-based cap-and-trade program. Incomplete regulation that exempts out-of-state producers achieves approximately a third of the emissions reductions achieved under complete regulation at more than twice the cost per ton of emissions abated.