The combined use of multi-sensory signals is often beneficial. Based on single cell recordings in the superior colliculius of cats, three basic rules were formulated to describe the effectiveness of multi-sensory integration: The enhancement of neuronal responses in multi- compared to uni-sensory conditions is largest when signals are presented at the same time ("temporal rule"), occur at the same location ("spatial rule"), and when signals are rather weak ("principle of inverse effectiveness"). These rules are also considered to describe multi-sensory benefits as observed with behavioral measures, but do they capture these benefits best? To uncover the principles that rule multi-sensory behavior, we investigated the classical redundant signals effect, i.e. the speed-up of response times in multi- compared to uni-sensory conditions. In a detection task, we presented both auditory and visual signals at three levels of signal strength and determined the speed-up for all nine combinations of signals. Based on a systematic analysis of empirical response time distributions as well as simulations using probability summation, we propose that two alternative rules apply. First, the "principle of equal effectiveness" states that the benefit with multi-sensory signals (here the speed-up of reaction times) is largest when performance in the two uni-sensory conditions is similar. Second, the "variability rule" states that the benefit is largest when performance in the uni-sensory conditions is variable. The generality of these rules is discussed with respect to experiments on accuracy and when maximum likelihood estimation instead of probability summation is considered as combination rule.