We have investigated a number of configuration interaction (CI) wave functions which incorporate the dominant effects of triple and quadruple substitutions. If we employ natural orbitals from a CI singles and doubles (CISD) procedure, then the orbitals may be conveniently partitioned into subspaces of varying importance, and electron configurations may be classified according to how they occupy each of the subspaces. We employ a CI model space containing all single and double substitutions and also those classes of triply and quadruply substituted configurations deemed most important on the basis of natural orbital populations. This a priori selection scheme recovers a large fraction of the energy of a CI including all triples and quadruples (CISDTQ) at a drastically reduced computational expense, and it represents a more ``black-box'' alternative to traditional multireference CI approaches. Implications for nonvariational approaches are also discussed.