A Monte Carlo study of five indices of dimensionality of binary items used a computer model that allowed sampling of both items and people. Five parameters were systematically varied in a factorial design: (1) number of common factors from one to five; (2) number of items, including 20, 30, 40, and 60; (3) sample sizes of 125 and 500; (4) nearly rectangular and highly peaked distributions of item difficulties; and (5) factor intercorrelations averaging in the thirties and in the fifties. Accuracy in distinguishing one factor from more than one was the criterion. An index involving variance-covariance matrices and based on the unidimensional property of local independence of items was overall most accurate. This index and an index based on ratios of differences in successive Eigenvalues were substantially more accurate in the peaked than in the rectangular distributions of item difficulties. An index based on the pattern of second principal factor loadings obtained in product-moment correlation matrices showed the reverse pattern. For all indices there is an increase in accuracy as both sample size and number of items is increased; for all indices there is a decrease in accuracy as factor intercorrelations are increased and as the number of factors is increased. (Author/LMO)