In this article the interaction of plane waves with a weak-contrast interface between two weakly anisotropic half-spaces is investigated. The anisotropy dealt with is of a general type. The stress-displacement vectors of the plane waves are calculated by perturbation theory. By assuming that the jump in elastic parameters and density across the interface is small, one can derive a simple expression for the RqPqP coefficient. In cases in which the wave motion is restricted to a symmetry plane of an anisotropic medium, simple expressions for the RqSVqSV and RSHSH coefficients are also derived.