A ring-laser gyroscope with the opposite modes coupled by an intracavity phase-conjugate interaction is examined analytically and numerically. It is shown that the coupling mitigates cross-saturation-induced mode extinction, allowing a homogeneously broadened medium to be used as the gain for a laser gyroscope. It is also shown that the coupling can induce a bias beat frequency that can potentially be used as an all-optical dither. The phase conjugation is shown to affect the lock-in threshold only indirectly. The results are compared with pertinent experiments from the literature.