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For some populations there may be two or more stratifying criteria that are desirable in the sample design. Multi-way stratification allows increased precision of estimates of each of the variables whose precision is increased by typical univariate estimators corresponding to single-criteria designs. The sample need not be allocated to every multi-way population cell induced by a set of single-criteria designs. As a special case, a solution to a problem posed in Neyman (1934) is presented.