We study the sovereign default model that has been used to account for the cyclical behavior of interest rates in emerging market economies. This model is often solved using the discrete state space technique with evenly spaced grid points. We show that this method necessitates a large number of grid points to avoid generating spurious interestrate movements. This makes the discrete state technique significantly more inefficient than using Chebyshev polynomials or cubic spline interpolation to approximate the value functions. We show that the inefficiency of the discrete state space technique is more severe for parameterizations that feature a high sensitivity of the bond price to the borrowing level for the borrowing levels that are observed more frequently in the simulations. In addition, we find that the efficiency of the discrete state space technique can be greatly improved by (i) finding the equilibrium as the limit of the equilibrium of the finite-horizon version of the model, instead of iterating separately on the value and bond price functions and (ii) concentrating grid points in asset levels at which the bond price is more sensitive to the borrowing level and in levels that are observed more often in the model simulations. Our analysis is also relevant for the study of other credit markets.