Balanced, nested (hierarchal) experimental designs are widely publicized and used to isolate and estimate variances associated with multi-stage processes. Beyond the two-stage design, there has been no information on the distributions of the estimates of variance components. This paper presents some initial results, mostly empirical, dealing with the distributions of the estimates of variance components derived from 5 × 2 × 2 × 2 balanced nested design. The results of a sampling study using eight different combinations of input variances is described and discussed. Normal, rectangular, and exponential parent populations were studied separately. Uncertainty associated with variance component estimation is shown to be intolerably great under certain commonly occurring conditions. The frequency of occurrence of negative estimates of variance components is emphasized.