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.