In this paper we present a new sampling scheme called the method of augmented sampling. The scheme is essentially a two sample procedure and is useful in surveys where all except one of the variates are similarly distributed and the distribution of the single variate differs markedly from the others. In the new method there is a basic sample in which we measure all the variates under enquiry. This sample is chosen so that the tolerances for all but one of the variates are met. A second sample is then drawn in which only one of the variates is measured. The size of the second sample is so determined that the tolerance for the remaining variate is met. A procedure for determining the sample sizes in each stratum such that this is achieved at a minimum cost is given.