Fellegi's (1974) improved method for estimating the interviewer component of correlated response variance is extended to a groups of k interviewer assignments for-general multistage survey designs. Using a linear models approach suggestive of Hartley and Rao (1978), the independence of the two estimators of interviewer variance is established and the forms of the variances of the estimators are derived. Then, using 1980 Census data-to compute terms in the estimator variances, (1) the optimal design of interviewer variance studies is considered, (2) the improvement of the composite estimator is demonstrated, and (3) some principles of efficient study design are developed.