  We investigate `non-local' schemes for baryogenesis at a first order
electroweak phase transition, in which the effects of a $CP$ violating
condensate on the bubble wall propagate into the unbroken phase where the
sphaleron rate is unsupressed. Such a condensate exists in multi-Higgs
extensions of the standard model, and may exist due to an instability in the
minimal standard model. In this paper we first discuss the general problem of
determining the $CP$ violating perturbations, distinguishing two regimes
(quantum and classical). We then give an analytic treatment of quantum
mechanical reflection in the thin wall regime, in which interactions with the
plasma can be neglected as a particle propagates across the wall. We focus on
leptons because of their much weaker coupling to the plasma. We argue that they
are likely to be accurately described by this calculation, but quarks are not.
The relative magnitude of the baryon asymmetry produced for different fermions
depends on their relative Yukawa couplings ({\it not} their zero temperature
masses), their transport properties and their interactions. We calculate the
baryon asymmetry for various parameter ranges and conclude that asymmetries
comparable with observations can be generated.
