We study constrained-efficient bank capital regulation in a model with market-imposed equity requirements. Banks hold equity buffers to insure against sudden loss of access to funding. However, in the model, banks choose to only partially self-insure because equity is privately costly. As a result, equity requirements are occasionally binding. Constrained-efficient regulation requires banks to build up additional equity buffers and compensates them for the cost of equity with a permanent increase in lending margins. When buffers are depleted, regulation relaxes the market-imposed equity requirements by raising bank future prospects through temporarily elevated lending margins.