  Using dimensional reduction we construct an effective 3D theory of the
Minimal Supersymmetric Standard Model at finite temperature. The final
effective theory is obtained after three successive stages of integration out
of massive particles. We obtain the full 1-loop relation between the couplings
of the reduced theory and the underlying 4D couplings and masses. The procedure
is also applied to a general two Higgs doublet model and the Next to Minimal
Supersymmetric Standard Model.
  We analyze the effective 3D theory constructed for the MSSM to determine the
regions of parameter space for which electroweak baryogenesis is possible. We
find that the inclusion of all supersymmetric scalars has the effect of
enhancing the strength of the phase transition. The requirement of a very light
stop is not necessary for baryogenesis. The phase transition is sufficiently
first order if the lightest Higgs mass, $m_{h} ~< 70$ GeV. We note the
existence of potentially interesting regions of parameter space for which
existing analysis techniques are inadequate to decide the question.
