Environmental policies with output-based refunding of the revenues effectively combine a tax on emissions with a subsidy to output. Three similar forms exist: tradable performance standards, an emissions tax with rebates, and tradable permits with output-based allocation. Two arguments for including an output subsidy are imperfect competition, in which an environmental regulation alone could exacerbate output underprovision, and imperfect participation, in which imposing a regulation on a subset of polluters could cause output to shift to exempt firms. However, both these scenarios imply that output shares among program participants are likely to be significant. In this situation, output-allocated permits offer less of a subsidy than a fixed rebate, and they can lead to inefficient shifting of production among participants. Rebating the emission tax reduces the incentive to abate, nor will marginal abatement costs be equalized if costs differ. These results hold in a Cournot duopoly model whether emission rates are determined simultaneously or strategically in a two-stage model.