Expressions for the shadow functions are derived for a broad class of non-Gaussian rough surfaces for which decorrelation of the surface heights implies statistical independence. The numerical results obtained for the backscatter shadow functions are compared with the shadow function for Gaussian surfaces and with recently published results for surfaces with an exponential joint height probability density that does not become statistically independent as the surface heights decorrelate. Contrary to earlier published results, it is shown that even for surfaces with large mean square slopes, the shadow function is not very sensitive to the precise form of the surface height density function assumed. This, however, does not mean that the rough surface scattering cross sections are insensitive to the assumed non-Gaussian surface height probability density.