Model selection is an omnipresent issue in structural equation modeling (SEM). When deciding among competing theories instantiated as formal statistical models, a trade-off is often sought between goodness-of-fit and model parsimony. Whereas traditional fit assessment in SEM quantifies parsimony solely as the number of free parameters, the ability of a model to account for diverse data patterns-known as fitting propensity-also depends on the functional form of a model. The present investigation provides a systematic assessment of the fitting propensity of models typically considered and compared in SEM, namely, exploratory and confirmatory factor analysis models positing a different number of latent factors or a different hierarchical structure (single-factor, correlated factors, higher-order, and bifactor models). Furthermore, the behavior of commonly used fit indices (CFI, SRMR, RMSEA, TLI) and information criteria (AIC, BIC) in accounting for fitting propensity was assessed. Although the results demonstrated varying degrees of fitting propensity for the models under scrutiny, these differences were mostly driven by the number of free parameters. There was little evidence for additional differences in the functional form of the compared models. Fit indices adjusting for the number of free parameters such as the RMSEA and TLI thus adequately accounted for differences in fitting propensity. (PsycInfo Database Record (c) 2022 APA, all rights reserved).