We discuss a two-dimensional model of a massive spinor field interacting via a derivative coupling with a massive pseudoscalar field. This model is exactly soluble in the zero-fermion-mass limit. We show that it is possible to treat the massive case in perturbation theory in such a way that no other couplings are induced and that the exactly soluble case is recovered smoothly upon turning off the fermion mass. This means in particular that the four-point function has a better ultraviolet behavior than that of its graphs individually.