Brown and Fisher (1972) proposed a model for subsampling mixtures of sampled material and used it to analyze an elementary composite sampling procedure. Their results and the results of Rohde (1976) are extended to cover procedures with several finite composites, testing error and within-increment variability. Among the properties of composite sampling procedures derived are the following: (1) the composite sampling estimator of a lot mean (μx) is unbiased whether or not the subsampling procedure in unbiased, (2) there is a relative upper bound on the variance of the composite sampling estimator of μx, and (3) it is not necessary to form more than one composite to check for changes in basic parameters from lot to lot. The impact of these and other properties on the process of choosing a composite sampling procedure is discussed.