In a complex sampling scheme it is desirable to select the primary sampling units (PSUs) without replacement to prevent duplications in the sample. Since the estimation of the sampling variances is more complicated when the PSUs are selected without replacement, L. Kish (1965) recommends that the variance be calculated using the formulas applicable for sampling with replacement. Kish states that this method probably leads to an overestimation of the true variance. This assertion, which is not self-evident, is investigated in this study. If the PSUs are selected in such a way that PSU "i" has a probability pi(sub i) equals nz(sub i) of being included in the sample, the population total is estimated unbiasedly. This is not the case if pi(sub i) is not equal to nz(sub i). For these two cases, various sampling procedures are considered. It is numerically verified that this assertion is true on average regardless of whether or not pi(sub i) equals nz(sub i). A sampling procedure for practical applications is recommended. There are 28 tables in the text and an additional 6 tables in 2 appendices. There is also a 25-item list of references. (Author/SLD)