This work extends previous studies on the perceptual asymmetry between the local maxima and minima of wide frequency modulations (FMs) [L. Demany and K. I. McAnally, J. Acoust. Soc. Am. 96, 706-715 (1994); L. Demany and S. Clement, J. Acoust. Soc. Am. 97, 2454-2459 (1995); L. Demany and S. Clement, J. Acoust. Soc. Am. 98, 2515-2523 (1995)]. In experiment 1, subjects had to discriminate frequency shifts in the temporally central vertex of V- and A-shaped FMs imposed on 200-ms sinusoidal tone bursts. The precise shapes of these FMs varied in eight steps from quasi-triangles (with a durationless central vertex) to quasi-squares (with a long-duration central vertex). The central vertex was either a minimum or a maximum, but in each case the corresponding frequency was near 1000 Hz and the FM span was about 0.5 oct. For each FM shape, the discrimination threshold was lower when the vertex was a maximum than when it was a minimum, but (in four subjects out of five) this difference decreased monotonically as the FM became less and less triangular. FM shape had a remarkably small effect on the discrimination of the maxima, and the thresholds measured for the sharpest maxima were unexpectedly low. In subsequent experiments, subjects had to discriminate frequency shifts in the starting point or the final point of unidirectional FMs (tone glides) that spanned about 0.5 oct in 100 ms. The relevant frequency extremum was near 1000 Hz in each condition. At the final point of the glides, discrimination was better for rising glides than for falling glides. At the starting point of the glides, discrimination was better for falling glides than for rising glides. Thus discrimination was always better when the relevant frequency extremum was a maximum than when it was a minimum, and this effect was produced both "forward" and "backward." The latter fact suggests that the perceptual asymmetry of FM originates at least partly from central factors.