To realize the benefits of item response theory (IRT), one must have model-data fit. One facet of a model-data fit investigation involves assessing the tenability of the conditional item independence (CII) assumption. In this Monte Carlo study, the comparative performance of 10 indices for identifying conditional item dependence is assessed. The relative performances of these indices are evaluated in terms of their Type I error rate, power, and false positive rate. Results show that the residual correlations approach and the "Q[subscript 3]" statistic can be considered as offering a reasonable compromise between maximum power and minimized false positive rates. (Contains 2 notes, 8 tables, and 2 figures.)