This paper examines the problem of defining and computing optimal capital requirements for insured banks. Such requirements are optimal when they make an arbitrarily fixed deposit insurance premium actuarially fair for each bank. Optimal capital requirements for insured banks are determined via the duality between the fair insurance premium and capital-to-deposit ratio. When a bank's initial capital position is not optimal, a capital infusion or an asset reshuffling is required to restore capital to the optimal level. The determination of the optimal capita1 infusion, considering different post-infusion asset reshuffling strategies, is also discussed. Numerical examples are developed to illustrate the properties of the model.