  In this paper we embed the light stop scenario, a MSSM framework which
explains the baryon asymmetry of the universe through a strong first order
electroweak phase transition, in a top-down approach. The required low energy
spectrum consists in the light SM-like Higgs, the right-handed stop, the
gauginos and the Higgsinos while the remaining scalars are heavy. This spectrum
is naturally driven by renormalization group evolution starting from a heavy
scalar spectrum at high energies. The latter is obtained through a
supersymmetry-breaking mix of gauge mediation, which provides the scalars
masses by new gauge interactions, and gravity mediation, which generates
gaugino and Higgsino masses. This supersymmetry breaking also explains the \mu\
and B_\mu\ parameters necessary for electroweak breaking and predicts small
tri-linear mixing terms A_t in agreement with electroweak baryogenesis
requirements. The minimal embedding predicts a Higgs mass around its
experimental lower bound and by a small extension higher masses m_H\lesssim 127
GeV can be accommodated.
