  We study the Minimal Messenger Model, a minimal version of Gauge Mediated
Supersymmetry Breaking models. Boundary conditions equal to zero for trilinear
and bilinear soft parameters at the messenger scale make this model free from
the supersymmetric CP problem and extremely predictive. These boundary
conditions and the vicinity of the messenger scale to the electroweak one,
require a careful implementation of the mechanism of radiative breaking of
$SU(2)\times U(1)$. We assess the importance of considering the complete
one-loop effective potential and of including a set of logarithmic two-loop
corrections to the B parameter for the correct determination of the electroweak
minimum. We analyze the resulting low-energy spectrum and give predictions of
interest for future experimental searches.
