Sek and Moore [J. Acoust. Soc. Am. 106, 351-359 (1999)] and Lyzenga et al. [J. Acoust. Soc. Am. 116, 491-501 (2004)] found that the just-noticeable frequency difference between two pure tones relatively close in time is smaller when these tones are smoothly connected by a frequency glide than when they are separated by a silent interval. This "glide effect" was interpreted as evidence that frequency glides can be detected by a specific auditory mechanism, not involved in the detection of discrete, time-delayed frequency changes. Lyzenga et al. argued in addition that the glide-detection mechanism provides little information on the direction of frequency changes near their detection threshold. The first experiment reported here confirms the existence of the glide effect, but also shows that it disappears when the glide is not connected smoothly to the neighboring steady tones. A second experiment demonstrates that the direction of a 750 ms frequency glide can be perceptually identified as soon as the glide is detectable. These results, and some other observations, lead to a new interpretation of the glide effect, and to the conclusion that continuous frequency changes may be detected in the same manner as discrete frequency changes.