The authors extend the surface-embedded Green function technique for calculating the electronic structure of surfaces and interfaces by presenting a method for determining substrate embedding potentials which makes no approximations to the substrate potential. They first present an alternative derivation of the surface-embedded Green function method, to clarify the use of a planar surface in simulating embedding on a more complicated surface and illustrate this with rigorous tests. Considering the case of a region embedded on two surfaces, they determine the conditions under which the resulting Green function may itself be used as a substrate-embedding potential, and thereby derive a procedure for obtaining an embedding potential which makes no approximation to the substrate potential. In the case of a substrate with semi-infinite periodicity this reduces to a self-consistency relation, for which they describe a first-order iterative solution. Finally, a particularly efficiency scheme for obtaining local properties within a surface or interface region is outlined. This constitutes a full-potential solution to the one-electron Schrodinger equation for systems of two-dimensional periodicity, whose calculation time scales linearly with the number of atomic planes.