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Cleaved coupled-cavity (C3) lasers are analyzed. Results are developed for longitudinal mode tuning and enhanced frequency modulation (FM) caused by amplitude modulation of the rear section. In addition, curves of laser segment versus modulator segment current at constant output power are calculated and residual amplitude modulation of the output power when operating in the FM mode is also determined. Both long-long and long-short C3devices are studied for strong, intermediate, and weak coupling between the segments. Because of the strong sensitivity to gap spacing, results are presented for many configurations which differ only by one-eighth wavelength in that dimension. This distance corresponds to a quarter wavelength in two passes. Analytic results are compared with previously published experimental observations.