We analyze a banking system in which the class of feasible deposit contracts, or mechanisms, is broad. The mechanisms must satisfy a sequential service constraint, but partial or full suspension of convertibility is allowed. Consumers must be willing to deposit, ex ante. We show, by examples, that under the so‐called “optimal contract,” the postdeposit game can have a run equilibrium. Given a propensity to run, triggered by sunspots, the optimal contract for the full predeposit game can be consistent with runs that occur with positive probability. Thus the Diamond‐Dybvig framework can explain bank runs as emerging in equilibrium under the optimal deposit contract.