The article shows that time-consistent, imperfectly targeted support to distressed institutions makes private leverage choices strategic complements. When everyone engages in maturity mismatch, authorities have little choice but intervening, creating both current and deferred (sowing the seeds of the next crisis) social costs. In turn, it is profitable to adopt a risky balance sheet. These insights have important consequences, from banks choosing to correlate their risk exposures to the need for macro-prudential supervision. (JEL D82, E52, E58, G01, G21, G28)