Perturbation and physical optics theories have traditionally been used to derive the scattering cross sections for composite surfaces that can be regarded as small-scale surface perturbations that ride on filtered, large-scale surfaces. In this case, perturbation theory accounts for Bragg scattering, while physical optics theory accounts for specular point scattering. However, for a more general class of composite surfaces that cannot be decomposed in such a manner, the perturbed–physical optics approach cannot be used. In these cases, it is shown, using the full wave approach, that the specular scattering associated with a filtered surface (consisting of the larger-scale spectral components) is strongly modified and that Bragg scattering and specular point scattering begin to blend with each other. Since the full wave solution accounts for Bragg scattering as well as specular point scattering in a self-consistent manner, it is not necessary to filter (decompose) the composite surface to evaluate the scattering cross sections in the general case. However, filtering the composite surface enhances one's physical insight as to the validity (or lack thereof) of the perturbed-physical optics decomposition and also facilitates the numerical evaluation of the scattering cross sections.