  A large class of non-minimal gauge mediation models, such as (semi-)direct
gauge mediation, predict a hierarchy between the masses of the supersymmetric
standard model gauginos and those of scalar particles. We perform a
comprehensive study of these non-minimal gauge mediation models, including mass
calculations in semi-direct gauge mediation, to illustrate these features, and
discuss the phenomenology of the models. We point out that the cosmological
gravitino problem places stringent constraints on mass splittings, when the
Bino is the NLSP. However, the GUT relation of the gaugino masses is broken
unlike the case of minimal gauge mediation, and an NLSP other than the Bino
(especially the gluino NLSP) becomes possible, relaxing the cosmological
constraints. We also discuss the collider signals of the models.
