The most dramatic physiological example of multisensory integration is response enhancement, where the integration of concordant signals across multiple sensory modalities leads to a larger and more reliable response. In the model system of the superior colliculus, the largest enhancements (often greater than the predicted sum) are observed when the individual signals being combined are weak. This principle conforms to expectations based on signal detection theory, and also as expected, enhancement is not uniform throughout any response. Typically it is greatest near its onset, when the unisensory inputs are at their weakest (Initial Response Enhancement, see Rowland et al., 2007; Rowland & Stein, 2008). Despite the general accuracy of this heuristic, however, there is a substantial amount of variance in the degree of observed enhancement at all levels of responsiveness. This observation appears to violate standard Bayesian predictions that are based on overall response magnitude. Aside from statistical noise, a possible explanation is that individual neurons in the dataset are calibrated to different "computational modes". An alternative hypothesis is that the amount of enhancement is influenced greatly by response properties other than magnitude, specifically, the temporal profile of the response. The present analysis advances the latter hypothesis. We present a mechanistic framework that explains these findings and extends the standard Bayesian approach to generate an accurate prediction for the multisensory response profile given known unisensory response profiles. These predictions offer a "null hypothesis" that can be used to quantify the circumstances and timing of anomalies in the integrative processes in different experimental conditions; for example, when it is developing under different conditions, or when it is disrupted by experimental or surgical intervention at any stage of life.