  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.
