Extending earlier work by MacCallum, Browne, and Sugawara (1996), procedures are shown for conducting power analysis of tests of overall fit of covariance structure models when null and alternative levels of model fit are specified in terms of values of the GFI or AGFl fit indexes. Results show that for GFI-based power analyses, holding null and alternative values of GFI fixed, power decreases as degrees of freedom increase, which is a counter-intuitive and undesirable phenomenon indicating lower power for detecting false null hypotheses about simpler models. For AGFI-based analyses, power increases as degrees of freedom increase. However, for both indexes it is shown that it is problematic to establish consistently appropriate values for null and alternative hypotheses about model fit. Because of these problems, it is recommended that the RMSEA index is preferable as a basis for power analysis and model evaluation.