Models of spontaneous CP violation can solve the Strong CP problem without the need of an anomalous Peccei-Quinn symmetry. In this work we review the Nelson-Barr approach, quantifying a peculiar coincidence between unrelated mass scales that these models must satisfy in order to correctly reproduce the Standard Model quark masses and CP violation. We investigate the compatibility between this requirement and the induced radiative corrections to the neutron electric dipole moment, and with bounds coming from collider, electroweak and flavor observables.