A system M is said to be a nicely nonlinear model of a given plant P if: i) M is tangent to P at the nominal equilibrium, ii) M is rigorously linearizable by output feedback. The present paper deals with the problem of identifying the parameters of a simple class of nicely nonlinear models. From a computational point of view, the problem to solve is a convex semi-infinite quadratic programming problem, for which a suitable algorithm has been set up.