Emission trading systems are cornerstone policies to reduce carbon emissions. Although economic intuition suggests that broader allowance trading should 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 impact total output. Finally, we provide evidence that this concern can 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/tCO.