When structural equation modeling (SEM) analyses are conducted, significance tests for all important model relationships (parameters including factor loadings, covariances, etc.) are typically conducted at a specified nominal Type I error rate ([alpha]). Despite the fact that many significance tests are often conducted in SEM, rarely is multiplicity control applied. Cribbie (2000, 2007) demonstrated that without some form of adjustment, the familywise Type I error rate can become severely inflated. Cribbie also confirmed that the popular Bonferroni method was overly conservative due to the correlations among the parameters in the model. The purpose of this study was to compare the Type I error rates and per-parameter power of traditional multiplicity strategies with those of adjusted Bonferroni procedures that incorporate not only the number of tests in a family, but also the degree of correlation between parameters. The adjusted Bonferroni procedures were found to produce per-parameter power rates higher than the original Bonferroni procedure without inflating the familywise error rate. (Contains 4 figures.)