Listeners have limited access to spatial information in lagging sound, a phenomenon known as discrimination suppression. It is unclear whether discrimination suppression works differently for interaural time differences (ITDs) and interaural level differences (ILDs). To explore this, three listeners assessed the lateralization (left or right) and detection (present or not) of lag clicks with a large fixed ITD (350 μs) or ILD (10 dB) following a diotic lead click, with inter-click intervals (ICIs) of 0.125-256 ms. Performance was measured on a common scale for both cues: the lag-lead amplitude ratio [dB] at 75% correct answers. The main finding was that the lateralization thresholds, but not detection thresholds, were more strongly elevated for ITD-only than ILD-only clicks at intermediate ICIs (1-8 ms) in which previous research has found the strongest discrimination suppression effects. Altogether, these findings suggest that discrimination suppression involves mechanisms that make spatial information conveyed by lag-click ITDs less accessible to listeners than spatial information conveyed by lag-click ILDs.