  We consider a solution to the mu problem in the context of Non-Minimal Gauge
Mediation with two Singlets and Low-Scale Messengers. This solution reduces
tuning associated with the "Little Hierarchy" problem by permitting a naturally
small mu term (100-300 GeV) due to small mixing between the Singlets. The
smallness of mu also relies crucially on compressing the Gauge Mediated
sparticle spectrum resulting in 330-400 GeV squarks. In addition to a small mu
term, the theory achieves a Higgs mass > 114.4 GeV through a large Higgs
quartic coupling when tanbeta ~ 1.5. The vacua studied are globally stable with
all couplings perturbative to the GUT scale. The amount of tuning required to
get the correct Electroweak scale is of order 10%, with a similar residual
tuning associated with the region of parameter space where the lightest CP-even
Higgs mass is above the LEP bound.
