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The paper is concerned with the causes and characteristics of threshold behavior in pulse-averaging and phase-coherent (``phase-locked loop'') FM subcarrier discriminators. An analytical discussion of the basic elements of each form of discriminator is first presented, leading to a comparison of the devices for input modulation indices of one and five, in the presence of noise. For the first time in the literature, the effect of additional output filtering following the ideal phase-coherent loop is discussed. Finally, the requisite modulation characteristics for an improved threshold in a phase-locked loop discriminator are presented, followed by a brief description of the approaches which may be taken in the design of such a system.