  We explore some topics in the phenomenology of gauge-mediated SUSY-breaking
scenarios having a large hierarchy of Higgs VEVs, $v_U/v_D = tan\beta \gg 1$.
Some motivation for this scenario is first presented. We then use a systematic,
analytic expansion (including some threshold corrections) to calculate the
$\mu$ parameter needed for proper electroweak breaking and the radiative
corrections to the B parameter, which fortuitously cancel at leading order. If
B = 0 at the messenger scale then $tan\beta$ is naturally large and calculable;
we calculate it. We then confront this prediction with classical and quantum
vacuum stability constraints arising from the Higgs-slepton potential, and
indicate the preferred values of the top quark mass and messenger scale(s). The
possibility of vacuum instability in a different direction yields an upper
bound on the messenger mass scale complementary to the familiar bound from
gravitino relic abundance. Next, we calculate the rate for $b\to s\gamma$ and
show the possibility of large deviations (in the direction currently favored by
experiment) from standard-model and small $tan\beta$ predictions. Finally, we
discuss the implications of these findings and their applicability to future,
broader and more detailed investigations.
