A major issue in the utilization of covariance structure analysis is model fit evaluation. Recent years have witnessed increasing interest in various test statistics and so-called fit indexes, most of which are actually based on or closely related to F[subscript 0], a measure of model fit in the population. This study aims to provide a systematic investigation about the performance of four available estimators of F[subscript 0]: a conventional estimator based on noncentral chi-square approximation; a newly proposed estimator that does not assume noncentral chi-square approximation; and two variations of the newly proposed estimator. A Monte Carlo simulation study is conducted to examine how these four estimators of F[subscript 0] perform across varying model misspecifications, data distributions, model sizes, and sample sizes. The results show that, under normality, all four quantities estimate F[subscript 0] equally well; and, under nonnormality, the three newly proposed estimators outperform the conventional estimator. Issues related to these findings are discussed.(Contains 6 tables.)