As a final remark, we would like to highlight that the full strength of the novel precomputed weighting scheme emerges when combined with the spin-adapted implementation of FCIQMC, based on the graphical unitary group approach (GUGA). This will be the subject of a future publication. In a series of recent works we have shown that by simple orbital localizations and reorderings it is possible to obtain CI Hamiltonian matrices with a unique and unprecedented block diagonal structure. As a consequence extremely compact wave functions (to the limit of near-single-reference) are obtained for ground and excited states of exchange-coupled poly-nuclear transition metal clusters. Since localized bases are propaedeutic to the GUGA wave function compression, it is clear that an excitation generator that exploits locality would further facilitate the screening of unnecessary excitation attempts in such sparse Hamiltonians. Our non-uniform drawing scheme in GUGA would promote those single and double excitations among nearest-neighbors and would screen out excitations that are related to decaying integral values, yielding efficiently sampled excitations in extremely sparse Hamiltonians.