We show that it is sometimes efficient for a bank to commit to a policy that keeps information about its risky assets private. Our model, based upon Diamond-Dybvig [1983], has the feature that banks acquire information about their risky assets before depositors acquire it. Banks have the option of using contracts where the middle-period return on deposits is contingent on this information, but by doing so they must also reveal the information. We derive the conditions on depositors' preferences and bankers' technology for which banks would prefer to keep information secret even though they must then use non-contingent deposit contracts.