  We show how to perform systematically improvable variational calculations in
the $O(2N)$ Gross-Neveu model for generic $N$, in such a way that all
infinities usually plaguing such calculations are accounted for in a way
compatible with the perturbative renormalization group . The final point is a
general framework for the calculation of non-perturbative quantities like
condensates, masses etc$\ldots$, in an asymptotically free field theory. For
the Gross-Neveu model, the numerical results obtained from a ``2-loop'' down to
low values of $N$.
