A weight of evidence is a calibrated statistic whose values in [0, 1] indicate the degree of agreement between the data and either of two hypothesis, one being treated as the null (H 0) and the other as the alternative (H 1). A value of zero means perfect agreement with the null, whereas a value of one means perfect agreement with the alternative. The optimality we consider is minimal mean squared error (MSE) under the alternative while keeping the MSE under the null below a fixed bound. This paper studies such statistics from a conditional point of view, in particular for location and scale models. © Springer-Verlag 2005.