This report is not intended as a stand-alone document. It is assumed that the reader has a basic understanding of Ernst (1986). Potential readers who do not, proceed at their own risk. It has been proposed that the expected overlap of sample PSUs be used as a criterion for selection of a stratification in the redesign for those household surveys that will maximize overlap of PSUs using the procedure of Ernst (1986). In general, computing the exact expected overlap for several stratifications that are being evaluated would require the impractical operation of running the entire overlap procedure for each stratum, for each stratification. A simple formula that provides a reasonable approximation to the overlap probability for each stratum in the new design would be a practical alternative. Such a formula, (2.4), is presented in this report. This formula requires that the initial and new stratifications be known, as well as the probability of selection for each PSU in the new design. (2.4) is an exact expression for the overlap probability when the new selection probability for each PSU in a new design stratum is equal to its initial selection probability. This formula will generally provide a good approximation to the overlap probability if the selection probabilities for the two designs are reasonably close.