In this Note an expression is derived for estimating the change in detector response due to perturbations in a fixed source system. This expression, developed with variational theory, includes a correction to first-order perturbation theory which accounts for the flux change caused by the perturbation. The derivation is extended to altered systems, and an expression is obtained which improves first-order perturbation theory by accounting for changes in the unaltered forward and adjoint fluxes. With this variational approach, all transport calculations can be performed in the unperturbed unaltered system.