A normal‐mode theory, for scattering of sound by the ocean surface in the presence of refraction, is reviewed. The theory is based on a perturbation expansion for small surface‐wave heights. New results, based on this theory, are presented for the Doppler‐shifted signal sidebands. These sidebands are the solution of the first‐order perturbation problem and are represented exactly by a double normal‐mode expansion with coefficients given by certain integral representations. The new results are derived by a saddle‐point analysis of the integral representations, due account being taken of the presence of singularities. Specific numerical results for the case of upward refraction are shown to display considerably more structure than in the case of an isovelocity ocean. The increased structure is explained in terms of the effects of backscatter and focusing through the use of wave‐number diagrams and ray‐trajectory constructions.