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For the prediction of the error probability performance of a digital frequency modulation (FM) receiver that uses a limiter-discriminator-integrator (LDI) detector, expressions for the rates of "clicks" are needed. Recently, formulas for FM click rates valid for the slow Rician fading channels have been derived by N.P. Secord et al. (see ibid., vol.42, p.197-204, 1993) by taking expectation of the classical click-rate formulas of Rice, which is valid for the additive white Gaussian noise (AWGN) channel, over the Rician distribution. We derive and present new closed-form expressions for average FM click rates for the fast Rician fading channels, taking into account the effect of Doppler spread or fading bandwidth. We exploit the fact that the multipath component of the Rician process can be combined with the AWGN into another Gaussian process, so that the classical click-rate analysis of Rice can be applied. An experiment using modern equipment is conducted, and the measured click rates match the theory closely for both the fast Rician and Rayleigh fading channels.