The general problem of sampling from multi-dimensional universes is considered where the object is to select samples that are representative of the universe in those characteristics held relevant and presumed known to some acceptable degree of accuracy as, for example, in the case of stratification. The object is to restrict the selection of samples to only those which are representative of the universe not only in each sample's dimensions but jointly as well, and to achieve this by meeting the usual requirements for probability sampling. Some schemes are presented, with algorithms for sample selection, which are possible alternatives to such schemes as quota sampling, deep stratification, controlled selection, lattice sampling and two-way stratification. The schemes can deal effectively with multi-dimensional universes with any degree of disproportionality in cell sizes including those with empty cells. Their adaptability to multi-stage sampling is indicated.