This paper shows that, when the price of emission allowances is sufficiently high, emission trading schemes improve the emission efficiency of highly polluting firms. The efficiency gain comes from a relative decrease in emissions rather than a relative increase in operating revenue. Part of the improvement is realized via the acquisition of green firms. The size of the improvement depends on the initial allocation of free emission allowances: highly polluting firms receiving more emission allowances for free, such as firms on the carbon leakage list, have a weaker incentive to become more efficient. For identification, we exploit the tightening in EU ETS regulation in 2017, which led to a steep price increase of emission allowances and made the ETS regulation more binding for polluting firms.