  The baryon number dissipation rate due to sphaleron transitions at high
temperatures in the minimal standard model is evaluated. We find that this rate
can be considerably suppressed by one loop contributions of bosonic and
fermionic fluctuations which are particularly important for a small mass of the
Higgs boson and a large top quark mass. Fixing the latter to its recently
stated value of 174 GeV the complete erasure of the baryon asymmetry is
prevented within the framework of the minimal standard model if the Higgs mass
is less than about 66 GeV.
