  We calculate the baryon asymmetry produced at the electroweak phase
transition by quasi-degenerate third generation sfermions in the minimal
supersymmetric extension of the Standard Model. We evaluate constraints from
Higgs searches, from collider searches for supersymmetric particles, and from
null searches for the permanent electric dipole moment (EDM) of the electron,
of the neutron and of atoms. We find that resonant sfermion sources can in
principle provide a large enough baryon asymmetry in various corners of the
sfermion parameter space, and we focus, in particular, on the case of large
$\tan\beta$, where third-generation down-type (s)fermions become relevant. We
show that in the case of stop and sbottom sources, the viable parameter space
is ruled out by constraints from the non-observation of the Mercury EDM. We
introduce a new class of CP violating sources, quasi-degenerate staus, that
escapes current EDM constraints while providing large enough net chiral
currents to achieve successful "slepton-mediated" electroweak baryogenesis.
