Structural equation modeling (SEM) attempts to remove the negative influence of measurement error and allows for investigation of relationships at the level of the underlying constructs of interest. SEM has been regarded as a "large sample" technique since its inception. Recent developments in SEM, some of which are currently available in popular SEM software programs, have lead to methods that may be more viable with small samples. While initial research investigating these methods shows promise, there is clearly the need for more thorough inspection to understand the behavior of these methods under varying experimental conditions. This study uses a Monte Carlo simulation experiment to explore the potential of these small sample methods for providing adequate model test statistics used in evaluating overall model fit. Type I error behavior and power were examined using maximum likelihood (ML), Satorra-Bentler scaled and adjusted (SB; A. Satorra and P. Bentler, 1988, 1994), residual-based (M. Browne, 1984), and asymptotically distribution free (ADF; M. Browne, 1982, 1984) test statistics. To accommodate small sample sizes, the ML and SB statistics were adjusted using a "k"-factor correction (M. Bartlett, 1950), and the residual-based and ADF statistics were corrected using modified chi-square and "F" statistics (K. Yuan and P. Bentler, 1998, 1999). Design characteristics include model type and complexity (15-variable structural equation and 21-variable confirmatory factor analysis models), sample size-to-estimated parameter ratio (n:q=1:1, 2:1, 5:1, and 10:1), and distributional form (normal and nonnormal, elliptically symmetric and asymmetric). (Contains 9 tables, 4 figures, and 33 references.) (SLD)