Orlando and Thissen (2000) introduced the "S - X[superscript 2]" item-fit index for testing goodness-of-fit with dichotomous item response theory (IRT) models. This study considers and evaluates an alternative approach for computing "S - X[superscript 2]" values and other factors associated with collapsing tables of observed and expected numbers (OE tables), which can affect flagging items. Results suggest that collapsing OE tables requires careful consideration of a trade-off between power and empirical type I error rate. Concurrent collapsing of score categories would be preferred over separate collapsing for its procedural simplicity, minimal effect of choice of a minimum cell value on empirical type I error rates, and reasonable type I error rates even for the most sparse condition in the study. For separate collapsing, a smaller minimum cell value is recommended as OE tables possess more sparseness (e.g., longer test lengths and smaller sample sizes) if inflated type I error rates are more of a concern in detecting items for misfit based on the "S - X[superscript 2]" index. If it is more important to identify misfit items, the study results recommend using a larger minimum cell value for collapsing.