When participants respond to stimuli of two sources, response times (RT) are often faster when both stimuli are presented together relative to the RTs obtained when presented separately (redundant signals effect, RSE). Race models and coactivation models can explain the RSE. In race models, separate channels process the two stimulus components, and the faster processing time determines the overall RT. In audiovisual experiments, the RSE is often higher than predicted by race models, and coactivation models have been proposed that assume integrated processing of the two stimuli. Where does coactivation occur? We implemented a go/no-go task with randomly intermixed weak and strong auditory, visual and audiovisual stimuli. In one experimental session, participants had to respond to strong stimuli, and withhold their response to weak stimuli. In the other session, these roles were reversed. Interestingly, coactivation was only observed in the experimental session in which participants had to respond to strong stimuli. If weak stimuli served as targets, results were widely consistent with the race model prediction. The pattern of results contradicts the inverse effectiveness law. We present two models that explain the result in terms of absolute and relative thresholds.