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Formulae are obtained for when the radar cross section (RCS) of a reflecting surface is smoothly averaged with respect to angle. Our results are derived using the physical optics approximation. The specific cases of near-broadside scattering from cylinders and flat plates are considered in detail. General results are derived for scattering from smooth surfaces in the high-frequency limit. It is shown that the high-frequency approximations to the smooth averages we employ are significantly more accurate than those previously obtained for hard-window averages. This should allow for more efficient and effective evaluations of dynamically collected RCS data. Analogous formulae for frequency averaging are also discussed.