  We present a simple scenario for gauge mediated supersymmetry breaking where
the messengers are also the fields that generate neutrino masses. We show that
the simplest such scenario corresponds to the case where neutrino masses are
generated through the Type I and Type III seesaw mechanisms. The entire
supersymmetric spectrum and Higgs masses are calculable from only four input
parameters. Since the electroweak symmetry is broken through a doubly radiative
mechanism, meaning a nearly zero B-term at the messenger scale which runs down
to acceptable values, one obtains quite a constrained spectrum for the
supersymmetric particles whose properties we describe. We refer to this
mechanism as "nu-GMSB".
