We show that for the simplest models of gauge mediated supersymmetry b
reaking, including all existing models, the true vacuum will not prese
rve QCD if it communicates supersymmetry breaking to the visible secto
r. We show that the desired supersymmetry breaking color preserving va
cuum can nonetheless be stable cosmologically, but only if certain cou
plings are sufficiently small. We also present simple modifications to
the sector which communicates supersymmetry breaking in which the tru
e vacuum is acceptable, suggesting desirable properties to be sought i
n dynamical models of supersymmetry breaking.