This study examines the use of the quasi-specular and two-scale models in estimating rough surface parameters from the average radar cross section of randomly rough surfaces, with the goal of understanding what scattering mechanisms limit their applicability. The ranges of validity of these models are ascertained by comparing the average backscattered normalized radar cross section given by the models to results obtained using an exact numerical Monte Carlo approach. The advantage of using a numerical solution is that the exact surface parameters are known quantities. The surfaces studied here are rough in only one dimension (that is, they are grooved in one dimension or corduroy). The height of the surfaces are Gaussian distributed and have either a Gaussian or a Pierson-Moskowitz spectrum. For surfaces with Gaussian spectra, it is found that the quasi-specular model can be used to obtain good estimates of the surface parameters when diffraction and multiple scattering effects are not important. Approximate validity conditions are established for this model. For surfaces with Pierson-Moskowitz spectra, it is found that the quasi-specular model can be used to obtain good estimates of the surface parameters for backscattering angles of less than 20°, and a two-scale model can be used for backscattering angles of up to at least 60°. However, the quasi-specular model must be modified to use only a portion of the surface spectrum, and this modification shows problematic dependence on the surface roughness, the incident wavelength, and the incident polarization. Of particular importance in the estimation problem are the numerical fluctuations present in the Monte Carlo simulation and the angular region over which data is compared to the model. Both of these factors are explored.