In a rational-expectations framework, we model depositors' confidence as a function of the probability of future bank bailouts. We analyze the effect of alternative bank bailout policies on depositors' confidence in an emerging market setting, where liquidity shortages of banks are revealed sequentially and governments cannot credibly commit to bailing out all potentially distressed banks. Our findings suggest that allowing early bank failures and using available liquidity for credible commitments to later bailouts can better boost confidence than early bailouts. This conclusion arises because with a high chance of liquidity shortage in the future, depositors may lose confidence and hence withdraw deposits even from potentially sound banks. Such a policy of late bailouts is likely to receive political support when a full bailout needs to be financed by taxation. The logic of late bailout remains valid even when banks may hide their distress or when closures of early distressed banks create contagion.