In applications of covariance structure modeling in which an initial model does not fit sample data well, it has become common practice to modify that model to improve its fit. Because this process is data driven, it is inherently susceptible to capitalization on chance characteristics of the data, thus raising the question of whether model modifications generalize to other samples or to the population. This issue is discussed in detail and is explored empirically through sampling studies using 2 large sets of data. Results demonstrate that over repeated samples, model modifications may be very inconsistent and cross-validation results may behave erratically. These findings lead to skepticism about generalizability of models resulting from data-driven modifications of an initial model. The use of alternative a priori models is recommended as a preferred strategy.