A new way of constructing uniformly better estimators (in the sense of minimum variance) from two independent unbiased estimators is presented. The problem of weighting estimators, when the ratio of their variances is unknown, is not straightforward. Yet this problem is particularly important in the recovery of inter-block information in balanced incomplete blocks. The theorem given in this paper suggests a simple method of constructing “better” estimators. The theorem has application in the analysis of balanced incomplete block designs; an example is given.