The mechanism(s) determining pitch may assign less weight to portions of a sound where the frequency is changing rapidly. The present experiments explored the possible effect of this on the overall pitch of frequency-modulated sounds. Pitch matches were obtained between an adjustable unmodulated sinusoid and a sinusoidal carrier that was frequency modulated using a highly asymmetric function with the form of a repeating U or inverted U shaped function. The amplitude was constant during the 400-ms presentation time of each stimulus, except for 10-ms raised-cosine onset and offset ramps. In experiment 1, the carrier level was 50 dB SPL and the geometric mean of the instantaneous frequency of the modulated carrier, fc, was either 0.5, 1, 2, or 8 kHz. The modulation rate (fm) was 5, 10, or 20 Hz. The overall depth (maximum to minimum) of the FM was 8% of fc. For all carrier frequencies, the matched frequency was shifted away from the mean carrier frequency, downwards for the U shaped function stimuli and upwards for the repeated inverted U shaped function stimuli. The shift was typically slightly greater than 1% of fc, and did not vary markedly with fc. The effect of fm was small, but there was a trend for the shifts to decrease with increasing fm for fc = 0.5 kHz and to increase with increasing fm for fc = 2 kHz. In experiment 2, the carrier level was reduced to 20 dB SL and matches were obtained only for fc = 2 kHz. Shifts in matched frequency of about 1% were still observed, but the trend for the shifts to increase with increasing fm no longer occurred. In experiment 3, matches were obtained for a 4-kHz carrier at 50 dB SPL. Shifts of about 1% again occurred, which did not vary markedly with fm. The shifts in matched frequency observed in all three experiments are not predicted by models based on the amplitude- or intensity-weighted average of instantaneous frequency (EWAIF or IWAIF). The shifts (and the pitch shifts observed earlier for two-tone complexes and for stimuli with simultaneous AM and FM) are consistent with a model based on the assumption that the overall pitch of a frequency-modulated sound is determined from a weighted average of period estimates, with the weight attached to a given estimate being inversely related to the short-term rate of change of period and directly related to a compressive function of the amplitude.