We study the optimal control of interbank contagion, when the government has complete information on interbank exposures. Financial institutions are prone to insolvency risk channeled through the network of exposures and to liquidity risk through bank runs. The government seeks to maximize, under budget constraints the total value of the financial system or, equivalently, to minimize the dead-weight loss induced by bank runs. The problem can be expressed as a convex optimization problem with a combinatorial aspect, tractable when the set of banks eligible for intervention is sufficiently, yet realistically, small