We analyse the efficiency effects of the initial permit allocation given to firms with market power in both permit and output market. We examine two models: a long- run model with endogenous technology and capacity choice, and a short-run model with fixed technology and capacity. In the long run, quantity pre-commitment with Bertrand competition can yield Cournot outcomes also under emissions trading. In the short run, Bertrand output competition reproduces the effects derived under Cournot competition, but displays higher pass-through profits. In a second-best setting of overallocation, a tighter emissions target tends to improve permit-market efficiency in the short run.