29 pagesWe show that in gauge mediation models where heavy messenger masses are provided by the adjoint Higgs field of an underlying SU(5) theory, a generalized gauge mediation spectrum arises with the characteristic feature of having a neutralino much lighter than in the standard gauge or gravity mediation schemes. This naturally fits in a hybrid scenario where gravity mediation, while subdominant with respect to gauge mediation, provides mu and B mu parameters in the TeV range