Two experiments are reported in which difference limens (DLs) were measured for onset times of a 1000-Hz tone pulse. An adaptive two-alternative forced-choice procedure and (mostly) well-trained subjects were used. In the first experiment, DLs were measured for the rise time of linear onset ramps at rise-time values between 10 and 60 msec. The DLs follow Weber's law up to a rise time of about 50 msec, and do not support the notion that rise times are perceived in a categorical manner. In the second experiment, DLs were obtained for linear, exponential, and raised-cosine onset envelopes at rise-time values between 10 and 40 msec. When energy differences in the critical band around 1000 Hz are computed for just-discriminable onsets, values between 0.7 dB (10-msec rise time) and 0.3 dB (40-sec rise time) are found. These equivalent intensity DLs show the same "near miss to Weber's law" behavior as do intensity DLs for pure tones.