Global and local methods are widely used in international macroeconomics to analyze incomplete-markets models. We study solutions for an endowment economy, an RBC model and a Sudden Stops model with an occasionally binding credit constraint. First-order, second-order, risky steady state and DynareOBC solutions are compared v. fixed-point-iteration global solutions in the time and frequency domains. The solutions differ in key respects, including measures of precautionary savings, cyclical moments, impulse response functions, financial premia and macro responses to credit constraints, and periodograms of consumption, foreign assets and net exports. The global method is easy to implement and faster than local methods for the endowment model. Local methods are faster for the RBC model and the global and DynareOBC solutions are of comparable speed. These findings favor global methods except when prevented by the curse of dimensionality and urge caution when using local methods. Of the latter, first-order solutions are preferable because results are very similar to second-order methods.