This study examined whether the level effects seen in monaural intensity discrimination (Weber's law and the "near miss") in a two-interval task are also observed in discrimination of interaural intensity differences (IIDs) in a single-interval task. Both tasks were performed for various standard levels of 4-kHz pure tones and broadband noise. The Weber functions (10 log ΔI/I versus I in dB) in the monaural and binaural conditions were parallel. For noise, the Weber functions had slopes close to zero (Weber's law) while the Weber functions for the tones had a mean slope of -0.089 (near miss). The near miss for the monaural and binaural tasks with tones was eliminated when a high-pass masker was gated with the listening intervals. The near-miss was also observed for 250- and 1000-Hz tones in the binaural task despite overall decreased sensitivity to changes in IID at 1000 Hz. The binaural thresholds showed a small (about 2-dB) advantage over monaural thresholds only in the broadband noise conditions. More important, however, is the fact that the level effects seen monaurally are also seen binaurally. This suggests that the basic mechanisms responsible for Weber's law and the near miss are common to monaural and binaural processing.