  We analyse the CP problem in the context of a supersymmetric extension of the
standard model with universal strength of Yukawa couplings. A salient feature
of these models is that the CP phases are constrained to be very small by the
hierarchy of the quark masses, and the pattern of CKM mixing angles. This leads
to a small amount of CP violation from the usual KM mechanism and a significant
contribution from supersymmetry is required. Due to the large generation mixing
in some of the supersymmetric interactions, the electric dipole moments impose
severe constraints on the parameter space, forcing the trilinear couplings to
be factorizable in matrix form. We find that the LL mass insertions give the
dominant gluino contribution to saturate epsilon_K. The chargino contributions
to epsilon'/epsilon are significant and can accommodate the experimental
results. In this framework, the standard model gives a negligible contribution
to the CP asymmetry in B-meson decay, a_{J/\psi K_s}. However, due to
supersymmetric contributions to B_d-\bar{B}_d mixing, the recent large value of
a_{J/\psi K_s} can be accommodated.
