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.