Pre-print, Working paper: Emission trading systems are cornerstone policies to reduce carbon emissions. Although economic intuition suggests that broader allowance trading should always be welfare improving, this paper proves that view can be wrong. Under an increasingly popular type of emissions trading scheme-tradable performance standards (TPS), multiple narrow markets can decrease emissions relative to a single unified market, so that restricting trade does not always harm welfare. We show analytically that, when intensity benchmarks are heterogeneous within a sector, this result can hold even if the well-known "implicit output subsidy" does not arise. Finally, we provide evidence that this concern is not a mere theoretical possibility but can actually be of high practical relevance. Using a general equilibrium model of China's TPS for 2020-2030, we show that broader trading results in significantly higher emissions (up to 10%), and decreases welfare relative to narrower markets when the social cost of carbon exceeds $91/tCO2 .