Several resonating-valence-bond-type states are being considered as an approximation of the two-hole ground state of the two-dimensional Hubbard-Anderson model. These states have been carefully constructed by Traa and Caspers with such algebraic properties, as to optimise different contributions of the Hubbard-Anderson hamiltonian. In this paper, the different contributions to their energies are calculated for lattices with sizes from 8 × 8 up to 16 × 16 and periodic boundary conditions, using a variational Monte-Carlo method. We show which state is lowest in energy and, more important, why this is so. In accordance with the optimal state from this tested set, we propose a bound state. It will be shown that this state is indeed the most stable state.