The discharge behavior of auditory-nerve fibers near "threshold" was investigated in anesthetized cats using low-intensity sinusoidal stimuli presented at the respective characteristic frequencies. Particular attention was paid to fibers with "low" and "medium" rates. Estimates of threshold derived from statistically significant increases in discharge rate indicate that the average threshold values for low-spontaneous fibers are only slightly higher (ca. 5 dB) than the averages for the corresponding high-spontaneous fibers, with the medium-spontaneous fibers having intermediate averages. The difference between these average values is considerably less than the more than 20-dB difference obtained using threshold criteria based on an absolute increment in discharge rate [e.g., M. C. Liberman, J. Acoust. Soc. Am. 63, 442-455 (1978)]. The main reason for the difference between the results of the two techniques is the fact that the slopes of the rate-intensity functions for the high-spontaneous fibers are considerably steeper near "threshold" than those for fibers of the other two classes. The results are taken as supportive of a recent model of primary-fiber discharge [C. D. Geisler, Brain Res. 212, 198-201 (1981)].