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The possible advantages of using algorithms that are minimum mean-square-error (MSE) optimal, or other averaging-type demodulators with frequency position modulation (FPM), are investigated. An attempt is made to describe the performance of the optimal and various suboptimal demodulators in terms of three parameters which depend on SNR and bandwidth expansion. The performance measures investigated are the reciprocal of the normalized mean-square error and the output SNR, which are different in the below-threshold region. The former is compared to the rate-distortion bound. The possible advantage of averaging-type discriminators from the point of view of the threshold is discussed.