Benchmark studies of H6, H7+, and H5+He were initiated in order to develop more efficient theoretical methods for describing the electron correlation energy, due to the relative ease with which the full configuration interaction (full CI) results could be obtained for these six-electron systems. Single-point energies which approach the quality of the full CI results are reported for a variety of coupled-cluster (CC) and configuration interaction (CI) methods using optimized basis sets and full CI optimized geometries. Emphasis is placed on multi-reference CI (MRCI) methods. By carefully limiting the configurations included in the CI and by using CI natural orbitals, we find it possible to reduce the number of configuration state functions (CSFs) by two orders of magnitude or more with little loss in the correlation energy recovered for the six-electron systems studied here. To judge the applicability of the MRCI methods to the study of potential energy surfaces, the energies of H2O at three geometries are compared to previously published full CI and complete active space self-consistent field (CASSCF) second-order CI (SOCI) results. Finally, we propose a compact MRCI wave function incorporating limited triple and quadruple excitations. Indirect tests suggest that this new approach should be highly effective.