Solving dynamic models with inequality constraints poses a challenging problem for two major reasons: dynamic programming techniques are reliable but often slow, whereas Euler equation-based methods are faster but have problematic or unknown convergence properties. This study attempts to bridge this gap. I show that a common iterative procedure on the first-order conditions – usually referred to as time iteration – delivers a sequence of approximate policy functions that converges to the true solution under a wide range of circumstances. These circumstances extend to a large set of endogenous and exogenous state variables as well as a very broad spectrum of occasionally binding constraints.