What determines the precision with which humans perceive the temporal order of events? Many theoretical models assume that temporal precision is limited by a central timing mechanism that compares the arrival time of incoming signals independent of peripheral events. This assumption was heavily inspired by early reports that temporal-order judgments are made with same precision for various intramodal and intermodal stimulus pairs. Experiment 1 tested whether intra- and intermodal jugments converge to a common threshold, at least after extensive practice. Five subjects performed 20 sessions of intramodal (two lights) and intermodal (light and tone) judgments in a ternary-response task, which allows a confound-minimized estimation of the thresholds. Critically, the intermodal temporal-order threshold was significantly higher than the intramodal temporal-order threshold across the entire practice curve. Nonetheless, it is conceivable that peripheral cues contribute to intramodal judgments, while the assumption of a stimulus-independent central processor still applies to intermodal judgments. Experiment 2 therefore tested whether stimulus intensity affects the intermodal temporal-order threshold. Specifically, 10 subjects performed five sessions of intermodal judgments in a ternary-response task, with light and sound being either dim and soft (low intensity) or bright and loud (high intensity). For most subjects, the intermodal temporal-order threshold decreased significantly with stimulus intensity. Taken together, both experiments provide evidence against the assumption that temporal precision is determined by a central timing mechanism that operates independently of peripheral events. This challenges many theoretical models of temporal-order perception.