Owing to effectiveness and ease of implementation Sum rule has been widely applied in the biometric research field. Different matcher information has been used as weighting parameters in the weighted Sum rule. In this work, a new parameter has been devised in reducing the genuine/imposter distribution overlap. It is shown that the overlap region width has the best generalization performance as the weighting parameter amongst other commonly used matcher information. Furthermore, it is illustrated that the equal weighted Sum rule can generally perform better than the Equal Error Rate and d-prime weighted Sum rule. The publicly available databases: the NIST-BSSR1 multimodal biometric and Xm2vts score sets have been used.