Despite the sensitivity of fit indices to various model and data characteristics in structural equation modeling, these fit indices are used in a rigid binary fashion as a mere rule of thumb threshold value in a search for model adequacy. Here, we address the behavior and interpretation of the popular Comparative Fit Index (CFI) by stressing that its metric for model assessment is the amount of misspecification in a baseline model and by further decomposition into its fundamental components: sample size, number of variables and the degree of multivariate dependence in the data. Simulation results show how these components influence the performance of CFI and its rule of thumb in practice. We discuss the usefulness of additional qualifications when applying the CFI rule of thumb and potential adjustments to its threshold value as a function of data characteristics. In conclusion, we at a minimum recommend a dual reporting strategy to provide the necessary context and base for meaningful interpretation and even more optimal, a move to using CFI as a real incremental fit index intended to evaluate the relative effect size of cumulative theoretically motivated model restrictions in terms of \% reduction in misspecification as measured by the baseline model.