Underwater acoustic communications channels involving surface reflection usually exhibit extensive time and frequency spreading. The phenomenon was studied in a recent paper [5] and the scattering function of the channel was obtained for large Rayleigh parameters using a Fresnel-corrected geometric optics model and a simple onedimensional surface correlation function. It was found that while extensive time spreading and Doppler were indeed predicted by this model, the Doppler shift and time delay were strongly correlated so that the scattering function had the form of a very narrow parabolic ridge. The problem considered in this paper is the extent to which this phenomenon persists when more realistic correlation-function models, dispersion, and small Rayleigh parameters are considered. It is found that the general form of the scattering function is not very much affected by fairly gross changes in the assumed surface statistics, and that substantial correlation between time delay and Doppler can be expected as long as the surface is not completely isotropic. The effect is also observed in a modified form with a small Rayleigh-parameter model, but since this model also features a strong coherent component it may be of less practical significance.