  We study the electroweak phase transition in the minimal extension of the
Standard Model: an extra complex singlet with zero vacuum expectation value.
The first-order phase transition is strengthened by the cubic term triggered in
the one-loop effective potential by the extra boson. Plasma effects are
considered to leading order: they shield the cubic terms and weaken the
first-order phase transition. We find a region in the parameter space where
baryon asymmetry washout is avoided for Higgs masses consistent with present
experimental bounds. However in that region the theory becomes non-perturbative
for scales higher than $10^{10}\ GeV$.
