  We study the interplay between the spontaneous breaking of a global symmetry
of the Higgs sector and gauge-mediated supersymmetry breaking, in the framework
of a supersymmetric model with global SU(3) symmetry. In addition to solving
the supersymmetric flavour problem and alleviating the little hierarchy
problem, this scenario automatically triggers the breaking of the global
symmetry and provides an elegant solution to the mu/Bmu problem of gauge
mediation. We study in detail the processes of global symmetry and electroweak
symmetry breaking, including the contributions of the top/stop and gauge-Higgs
sectors to the one-loop effective potential of the pseudo-Goldstone Higgs
boson. While the joint effect of supersymmetry and of the global symmetry
allows in principle the electroweak symmetry to be broken with little
fine-tuning, the simplest version of the model fails to bring the Higgs mass
above the LEP bound due to a suppressed tree-level quartic coupling. To cure
this problem, we consider the possibility of additional SU(3)-breaking
contributions to the Higgs potential, which results in a moderate fine-tuning.
The model predicts a rather low messenger scale, a small tan beta value, a
light Higgs boson with Standard Model-like properties, and heavy higgsinos.
