We propose a simple and fast ˝xed-point iteration algorithm (FiPIt) to obtain the global, non-linear solution of macro models with two endogenous state variables and occasionally binding constraints. This method uses ˝xed-point iteration on Euler equations to avoid solving two simultaneous non-linear equations (as with the time iteration method) or creating modi˝ed state variables requiring irregular interpolation (as with the endogenous grids method). In the small-open-economy RBC and Sudden Stops models provided as examples, FiPIt is much faster than time iteration and various hybrid methods.