In 1943 Wald [2] gave a method for constructing tolerance regions in the multivariate case. Tukey generalized Wald's procedure in [4] and the results were interpreted for discontinuous distributions in [5] and [6]. This paper presents a further generalization of the method so that statistically equivalent blocks can be determined sequentially; the particular function used to cut off a block may depend on the shape or structure of previously selected blocks. The results are also interpreted for the case of discontinuous distributions. Possible advantages of applying the method are discussed.