In a previous paper, we have avoided an infinite order perturbation expansion and obtained a closed expression which consists of the second-order Moller-Plesset energy component together with a remainder term. The applicabilty of second-order many-body perturbation theory with a Moller-Plesset reference hamiltonian then rests upon the magnitude of this remainder term rather than the behaviour of the higher order terms on the perturbation series. In the present work, we show how this remainder term can be estimated by limited configuration interaction.