Diamond and Rajan (J Finance 55:2431–2465, 2000; Am Econ Rev Papers Proc 91:422–425, 2001a; Carnegie–Rochester Conf Series Public Policy 54:37–71, 2001b; J Pol Econ 109:287–327, 2001c) have shown in a series of papers that it is precisely the fragility of their capital structure which allows banks to create liquidity. This is because the threat of runs by depositors forces bankers to extract full repayment on otherwise illiquid assets. This result has important implications for financial regulation, such as for capital requirements and deposit insurance. This note shows that put options held by bank owners dominate deposit financing in that they also discipline bankers but do not give rise to inefficient runs. Fragility is thus not necessary for liquidity creation in the Diamond–Rajan framework.