More on Electric Dipole Moment Constraints on Phases in the Constrained MSSM

We reconsider constraints on $\cp$-violating phases in the Constrained Minimal Supersymmetric Standard Model. We include the recent calculations of Ibrahim and Nath on the chromoelectric and purely gluonic contributions to the quark electric dipole moment and combine cosmological limits on gaugino masses with experimental bounds on the neutron (and electron) electric dipole moments. The constraint on the phase of the Higgs mixing mass $\mu$, $|\thm|$, is dependent on the value of the trilinear mass parameter, $A$, in the model and on $\tan \beta$. For values of $|A| < 300 \gev$ at the GUT scale, we find $|\thm|/\pi \la 0.05$, while for $|A| < 1500 \gev$, $|\thm|/\pi \la 0.3$. Thus, we find that in principle, large CP violating phases are compatible with the bounds on the electric dipole moments of the neutron and electron, as well as remaining compatible with the cosmological upper bound on the relic density of neutralinos. The other $\cp$-violating phase $\tha$ is essentially unconstrained.