We calculate the baryon asymmetry produced at the electroweak phase transition by quasidegenerate 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 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 tanβ, where third-generation down-type (s)fermions become relevant. We show that in the case of top squark and sbottom sources, the viable parameter space is ruled out by constraints from the nonobservation of the Mercury electric dipole moment. We introduce a new class of CP-violating sources, quasidegenerate staus, that escapes current electric dipole moment constraints while providing large enough net chiral currents to achieve successful slepton-mediated electroweak baryogenesis.