Localized changes in a reacting system generally lead to a recomputation of neutronic behavior. The calculation involved can be simple (first-order perturbation theory applied for small changes), or complex (a complete system-wide recomputation for large alterations). In this paper, we consider changes in an isolated portion of a system, changes that are too large for accurate prediction using first-order perturbation theory. Unless the alteration is excessively large, we should still expect the neutron distribution a few mean-free-paths from the altered region to change only slightly. We exploit the idea that localized changes can be dealt with more simply by decoupling the altered region (including a buffer zone) from the rest of the system. The spatial magnitude of the recomputation can then be reduced, with concomitant savings in effort and cost. Variational methods are used to predict the shift in k to second order. As an additional bonus, first-order estimates of the change in the flux and adjoint are calculated.