Electroweak baryogenesis can occur in the ''adiabatic limit'', in whic
h expanding bubbles of true vacuum are assumed to have rather thick wa
lls and be slowly moving. Here the problem of calculating the baryon a
symmetry in this limit is reconsidered. A simple prescription for obta
ining the relevant kinetic equations is given. An additional suppressi
on beyond that usually assumed is found. This arises because the gener
ation of an asymmetry requires violation of approximately conserved cu
rrents by Higgs expectation values, which are small near the front of
the walls. As applications, the asymmetries in multi-Higgs models and
the minimal supersymmetric standard model are estimated to be proporti
onal to alpha(w)8 and alpha(w)6 respectively. Also, in this limit the
baryon asymmetry in the minimal standard model is extraordinarily smal
l.