  In this note we elaborate on a recent counter-example to the Nelson-Seiberg
theorem and to its generalizations. We provide sufficient conditions for the
existence of such counter-examples, finding new ones. We claim that these
counter-examples are connected with the presence of pairs of fields with
opposite R-charge getting a VEV. Furthermore we comment on the "non-genericity"
of our models, showing that none of them violates the original Nelson-Seiberg
theorem
