The average field of an electrical dipole of arbitrary orientation, placed over a statistically rough sphere with a small surface impedance, is analyzed using Bourret's approximation. The isotropic and statistically uniform inhomogeneities are assumed to be small and smooth, which allows the use of a perturbation theory in the boundary conditions. Effective reflection coefficients for spherical waves are calculated, the analytical properties of which allow application of the Watson method for an asymptotic analysis of the average field in the illuminated region and in the shadow.