We study gauge-mediated theories containing several messengers with th
e most general SU(5)-invariant mass and supersymmetry-breaking paramet
ers. We show that these theories are predictive, containing only two r
elevant parameters more than the minimal gauge-mediated model. Hyperch
arge D-terms can contribute significantly to the right-handed charged
sleptons and bring them closer in mass to the left-handed sleptons. Th
e messenger masses must be invariant under either SU(5) or a ''messeng
er parity'' to avoid spontaneous breaking of charge conservation.