We give an intuitive proof of a new non-renormalization theorem in sup
ersymmetric field theories. It applies both perturbatively and non-per
turbatively. The superpotential is not renormalized in perturbation th
eory but receives non-perturbative corrections. However, these non-per
turbative corrections are not generic functions of the fields consiste
nt with the symmetries. Certain invariant terms are not generated. Thi
s violation of naturalness has applications to dynamical supersymmetry
breaking.