  We find using the minimal left-right symmetric model that the presence of
leptonic CP violation can radiatively generate a strong CP phase at the
one-loop level itself, which can be beyond the current bounds established by
the neutron electic dipole moment experiments. If there are no axions or
unnatural cancellations, this leads to the testable prediction that leptonic CP
violation must be negligibly small (Dirac phase $\delta_{CP} = 0$ or $\pi$), in
a wide and interesting region of parameter space.
