In widely frequency modulated sine tones, frequency maxima are perceived more accurately than frequency minima: A shift in a local frequency extremum is better detected when the extremum is a maximum than when it is a minimum, even within the same spectral region [L. Demany and K. I. McAnally, J. Acoust. Soc. Am. 96, 706-715 (1994)]. It is reported here that this perceptual asymmetry is about equally strong for frequency extrema near 250 and 1000 Hz, but weaker near 4000 Hz. It was also found that near 1000 Hz, the asymmetry is about equally strong for stimuli with an SPL of 35 and 70 dB, although the neural excitation patterns of a 1000-Hz tone probably have a different shape--and more specifically a different asymmetry--at these two levels. Finally, stimulus uncertainty was found to reduce the perceptual asymmetry: A weaker asymmetry was measured when the standard frequency extremum varied randomly from trial to trial than when it was fixed. The latter result, and the fact that the asymmetry did not decrease with training in the discrimination task, suggest that the asymmetry cannot be counteracted by "top-down" attentional processes and may be a preattentional phenomenon.