if The weight function w can be a powerful tool. However, if misused, we suspect that it could be dangerous. In particular, if little or no weight is given to a certain region of the parameter space, we should not expect the resulting weighted interval estimator to perform well in this region. This was observed in Section 4.1.where we saw in Fig. 3that the coverage p large dramatically tails off near 1 because the weight approaches approaches 1. Of course, this poor performance for In might welcomed in exchange for the enhanced performance for small values hich were given more weight. this paper, we have focused on the mean expected and the mean coverage probability as a means to address optimality. However, other optimality criterion could have been used to define the "best" interval. For example, an interval estimator might be deemed meritorious if its coverage probability does not typically deviate far from 1 a If so, we could select the interval whose mean coverage probability deviation is the smallest It is not our goal to suggest that one particular interval or measure of merit is best. Instead, our main goal is to suggest that "merit" can be precisely defined and that the optimal interval estimator can be constructed accordingly.