When redesigning a survey with a multi-stage design, it is sometimes desired to maximize the number of first stage units retained in the new sample without altering unconditional selection probabilities. Using transportation theory, an optimal solution to this problem for a very general class of designs was recently presented by Causey, Cox and Ernst. However, that procedure has not yet been used in the redesign of any survey because it requires the knowledge of certain joint probabilities which are often not known in practice. In this paper an alternative linear programming procedure is presented which requires only probability information that should always be available, and which, under certain conditions, is optimum among all procedures requiring only this information. This procedure has recently been used in the redesign of two major surveys conducted by the U.S. Bureau of the Census, the Current Population Survey, and the National Crime Survey.