We compute the tunneling probability from the symmetric phase to the t
rue vacuum, in the first-order electroweak phase transition of the MSS
M, and the corresponding Higgs profiles along the bubble wall. We use
the resummed two-loop temperature-dependent effective potential, and p
ay particular attention to the light stop scenario, where the phase tr
ansition can be sufficiently strongly first-order not to wipe off any
previously generated baryon asymmetry. We compute the bubble parameter
s which are relevant for the baryogenesis mechanism: the wall thicknes
s and dp. The two-loop corrections provide important enhancement effec
ts, with respect to the one-loop results, in the amount of baryon asym
metry. (C) 1998 Elsevier Science B.V.