  We study electroweak baryogenesis and electric dipole moments in the presence
of the two leading-order, non-renormalizable operators in the Higgs sector of
the MSSM. Significant qualitative and quantitative differences from MSSM
baryogenesis arise due to the presence of new CP-violating phases and to the
relaxation of constraints on the supersymmetric spectrum (in particular, both
stops can be light). We find: (1) spontaneous baryogenesis, driven by a change
in the phase of the Higgs vevs across the bubble wall, becomes possible; (2)
the top and stop CP-violating sources can become effective; (3) baryogenesis is
viable in larger parts of parameter space, alleviating the well-known
fine-tuning associated with MSSM baryogenesis. Nevertheless, electric dipole
moments should be measured if experimental sensitivities are improved by about
one order of magnitude.
