This paper develops a model of the lender of last resort. It provides an analytical basis for “too big too fail” and a rationale for “constructive ambiguity”. Key results are that if contagion (moral hazard) is the main concern, the Central Bank (CB) will have an excessive (little) incentive to rescue banks and the resulting equilibrium risk level is high (low). When both contagion and moral hazard are jointly analyzed, the CB’s incentives to rescue are only slightly weaker than with contagion alone. The CB’s optimal policy may be non-monotonic in bank size.