The quasi-specular and two-scale models for the average radar cross section of randomly rough surfaces have seen extensive use in inversion algorithms to estimate surface roughness parameters. This paper and a companion paper report the results of a numerical study on the accuracy of these models which was initiated with the goal of understanding what scattering mechanisms limit their applicability. In this paper, surfaces which are Gaussian distributed in height and have Gaussian spectra are examined. It is shown that the quasi-specular model is limited by multiple scattering and diffraction due to surface curvature. The effects of polarization and the role of the surface dielectric constant are examined at length. Approximate conditions for which the quasi-specular model is valid are provided. ¿ 1998 American Geophysical Union