We introduce a method for computing simple energy-conserving model T-matrices intended for use in multiple-scattering formalisms. Our method is to make separable approximations to the physical scattering potentials. Such a `mean-field' approximation permits a ready analytic evaluation of the T-matrix for a variety of scatterers, even `fuzzy' scatterers (e.g. fractal aggregates). In the small-size limit, our method reduces to the point-like resonant T-matrix introduced by Nieuwenhuizen et al in 1992 thereby demonstrating the intrinsic mean-field nature of their approximation. We discuss causality in both models and show that the separable potential model possesses a wider range of applicability than the point-like model does.