Boundary value integral equations and the moment method solution technique provide a succinct and elegant strategy for the solution of acoustic surface scattering problems. This paper explores the application of a subdomain basis set, based on the phase of the incident radiation, which is used to solve for the unknown normal pressure gradient on the surface of the scatterer using the moment method. The advantage of this basis set lies in the fact that it can accurately represent the fast phase character of the pressure gradient on the surface of the scatterer. This allows for far fewer discretizations/basis elements in the moment method formulation and therefore significantly reduces the density of unknowns that must be numerically computed. The main contribution of this paper is to show how to efficiently employ this natural basis and to explore the physical justification for using this approach. The method is compared with other techniques including the Kirchhoff solution technique, high frequency single scattering techniques, the Nussenzveig–Fock technique, and the parabolic equation approximation. Unlike these methods no approximation to the physical system need be introduced.