Assessing whether a multiple-item scale can be represented with a one-factor model is a frequent interest in behavioral research. Often, this is done in a factor analysis framework with approximate fit indices like RMSEA, CFI, or SRMR. These fit indices are continuous measures, so values indicating acceptable fit are up to interpretation. Cutoffs suggested by Hu and Bentler (1999) are a common guideline used in empirical research. However, these cutoffs were derived with intent to detect omitted cross-loadings or omitted factor covariances in multifactor models. These types of misspecifications cannot exist in one-factor models, so the appropriateness of using these guidelines in one-factor models is uncertain. This paper uses a simulation study to address whether traditional fit index cutoffs are sensitive to the types of misspecifications common in one-factor models. The results showed that traditional cutoffs have very poor sensitivity to misspecification in one-factor models and that the traditional cutoffs generalize poorly to one-factor contexts. As an alternative, we investigate the accuracy and stability of the recently introduced dynamic fit cutoff approach for creating fit index cutoffs for one-factor models. Simulation results indicated excellent performance of dynamic fit index cutoffs to classify correct or misspecified one-factor models and that dynamic fit index cutoffs are a promising approach for more accurate assessment of model fit in one-factor contexts.