A Monte Carlo simulation was conducted to investigate the Type I error rates of several versions of chi-square difference tests for nonnormal data in confirmatory factor analysis (CFA) models. The studied statistics include the uncorrected maximum likelihood (ML) difference test, D; the original robust difference test, (Satorra & Bentler, 2001); and the recent modification to this test, , which ensures that the statistic remains positive (Satorra & Bentler, 2010). A hybrid procedure that only computes when is negative was also included, but its performance was nearly identical to . Types of constraints studied included constraining factor correlations to 0, constraining factor correlations to 1 (testing a model with fewer factors), constraining loadings to equal each other within or across factors, and testing for the presence of cross-loadings. The robust tests performed well and similarly to each other in many conditions. The new strictly positive test, exhibited slightly inflated rejection rates in some conditions, particularly at small sample sizes, and the original robust test exhibited rejection rates below nominal in many conditions, which sometimes remained low even at the highest studied sample size.