This paper studies bank competition with borrower adverse selection. In the model, expected non-performing loan costs are high when credit is granted in booms, when risk free rates are low, or when competition is strong. I prove that full competition is suboptimal due to this last effect; that more competition improves the transmission of monetary policy, and that lending rates are always pro-cyclical. The paper examines the relative plausibility of sequential and simultaneous bank competition. I show that with asymmetric costs, bank market shares are always inversely related to their efficiency, and that bank entry does not always lower lending rates.