After a brief review of gauge mediation of supersymmetry breaking, we consider a class of models where there are several hidden sectors, completely decoupled if the visible sector couplings are set to zero. One expects a Goldstino to arise in each SUSY breaking sector, however only one will eventually become the longitudinal polarization of the gravitino. We set out to compute the radiatively induced mass of the other combinations, a.k.a. the Pseudo-Goldstini. We first show that the effective theory is not very useful to this purpose. Instead, we can use a formalism very similar to the one of General Gauge Mediation to write an exact and completely general expression for this mass. In a specific, calculable model, it arises at three loops. The result yields a phenomenologically interesting NLSP pseudo-Goldstino at 1-100 GeV.
