  We give an intuitive proof of a new non-renormalization theorem in
supersymmetric field theories. It applies both perturbatively and
non-perturbatively. The superpotential is not renormalized in perturbation
theory but receives non-perturbative corrections. However, these
non-perturbative corrections are {\it not} generic functions of the fields
consistent with the symmetries. Certain invariant terms are not generated. This
violation of naturalness has applications to dynamical supersymmetry breaking.
