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Correlative phase shift keying (CORPSK) is described. CORPSK is a constant envelope modulation technique with smooth transitions between fixed phase positions with successive transitions correlated. A number of CORPSK members for 2 and 4 input levels are analyzed, including tamed frequency modulation (TFM). Main lobe bandwidth is the same or less than in other constant envelope modulation techniques such as MSK, QPSK, and CPFSK, but the out-of-band radiation is much lower. Carrier extraction can be realized with simple techniques, so that coherent detection with optimum receiver performance is practically feasible. Simulation results are presented for coherent as well as noncoherent detection. A power efficiency 2 dB better than four MSK and DQPSK can be obtained for CORPSK with no more than for phase positions. A wide variety of modulations exists within the CORPSK class, with ample opportunity for tradeoffs between power, bandwidth, and complexity. Practical results for TFM are reported.