A reduced-order algorithm for the smoothing of the complementary states of a linear system is developed. If there are l complementary states to be estimated, the smoothing problem using the reduced-order algorithm involves solving a hamiltonian system of equations of order 2l as compared to an order of 2n for full-order smoothing. We also obtain realizations for fixed interval smoothing using a two-filter structure, fixed point, and fixed lag smoothing. Equivalent filtering and smoothing problems for the discrete case are also discussed. Finally, an example is presented to show that the reduced-order algorithms perform quite satisfactorily compared to the optimal full-order Kalman-type algorithms. Given the computational savings, reduced-order complementary estimators might prove to be useful in situations where computation and memory limitations are an important factor.