This article builds on the work of Savalei and Bentler (2009), who proposed and evaluated a statistically justified two-stage (TS) approach for fitting structural equation models with incomplete normally distributed data. The TS approach first obtains saturated maximum likelihood (ML) estimates of the population means and covariance matrix and then uses these saturated estimates in the complete data ML fitting function. Standard errors and test statistics are then adjusted to reflect uncertainty due to missing data. This work presents an extension of the TS methodology to nonnormal incomplete data (robust TS) and conducts an empirical evaluation of its performance relative to the full information maximum likelihood (FIML) approach with robust standard errors and a scaled chi-square statistic. The results indicate that although TS parameter estimates are slightly lower in efficiency, the TS approach performs better than FIML in terms of coverage and the rejection rate of the scaled chi-square across a wide variety of conditions. Its wide implementation and further study are encouraged.