After repeated exposure to a pair of audiovisual stimuli with a constant lag, subjects eventually judge the pair as occurring simultaneously (lag adaptation). In contrast, perceptual changes occur in the opposite direction with tactile stimuli, delivered one to each hand, which conforms to a Bayesian integration theory. Several recent studies have examined the calibration of simultaneity in regard to sound and touch, and light and touch, but results remain at odds with each other. These findings may seem confusing, but they become more reasonable assuming that both mechanisms operate in the brain. We previously showed, in theory, that the effect of Bayesian calibration cannot be observed when the lag adaptation was fully operational. This led us to hypothesize that Bayesian calibration is at work even during judgments regarding audiovisual temporal order, but that the effect is concealed behind the lag adaptation mechanism. In our recent study, we have shown that this was the case. By "neutralizing" lag adaptation by using two pitches of sounds, we successfully uncovered Bayesian calibration that was working behind lag-adaptation. From the results and the theoretical considerations, we propose a serial model that combines lag adaptation and Bayesian calibration and suggest that the size and direction of shift in the point of simultaneity ranges from full lag adaptation to full Bayesian calibration, depending on the strength of lag adaptation.