A weighted sampling method for single excitations has been presented that uses precalculated probabilities. The weights for single excitations are obtained by contracting over all orbitals in the two-electron term, rather than over only the occupied ones. This approximation works particularly well for localized orbitals, where it can take advantage of the exponential decay of integrals with increasing spatial distance. Precisely in the localized basis single excitations are pivotal for efficient FCIQMC dynamics, hence right when weighted sampling of single excitations becomes relevant our approximation works well.