Pair correlations and the effects of dense packing are included to extend existing results on reflection and scattering by distributions of protuberances (bosses) on rigid or free base planes. The earlier energy conserving forms for the specularly reflected wave, the surface impedance, and the differential scattering cross section per unit area, are obtained in terms of a transform of the scattering amplitude of an isolated boss. Low‐frequency approximations are developed with emphasis on the roles of the packing density and multipole coupling effects, and explicit results are given for semi‐elliptic cylinders and hemi‐ellipsoids. For lossless bosses, the reflection coefficient has a minimum, and the incoherent scattering a maximum, at the packing density corresponding to maximum fluctuations in the number of bosses per unit area. Multipole coupling effects may be misinterpreted in data inversion programs as changes in boss shape; if such effects are not included, then, e.g., hemispheres may be mistaken for hemiellipsoids broadened along the base plane and shortened along the normal.