Covariance structure analytic techniques have become increasingly popular in recent years. During this period, users of statistical software packages have become more and more sophisticated, and more and more researchers are wanting to make sure that they are using the "best" statistic, whether it be for small sample considerations or for issues of nonnormality. At present, none of the confirmatory structure analytic programs include small sample modifications such as the k-factor Bartlett multiplier (1950) or the Swain multiplier (A, Swain, 1975). They do however include modifications to address distributional nonnormality. EQS offers the Satorra-Bentler scaled statistics (A. Satorra and P. Bentler, 1988, 1989); it does not yet offer the Satorra-Bentler adjusted statistic. AMOS, on the other had, offers a bootstrap alternative, however, it does not yet offer either of the Satorra-Bentler modified statistics. This Monte Carlo study addresses whether resampling-based procedures provide improved Type I error control over the modified test statistics such as the k-factor Bartlett modified, Swain modified, Satorra-Bentler scaled, and Satorra-Bentler adjusted test statistics. The study provides evidence on the relative performance of the Beran-Strivastave bootstrap procedure and demonstrates that this procedure does not provide as good control of Type I error under conditions of extremely mild distributional nonnormality as the 0-factor Bartlett or Swain modified maximum likelihood procedure. It does show improved Type I error control over the standard maximum likelihood procedure. (Contains 7 tables, 6 figures, and 42 references.) (Author/SLD)