It would be difficult to deny the claim that the most contentious issue in Rasch measurement is that of fit. Outside Rasch measurement circles, we continue to perplex the rest of the psychometric world by insisting that our task is to produce empirical data that fit the Rasch model’s specification. Others in IRT talk of fit in what many consider to be conventional terms (i.e., how well does the model fit the data). Of course, the concept of fit must be considered hand in hand with the requirements for unidimensionality, equal discrimination, and local independence of items. The concept of unidimensionality reflects the Rasch model’s focus on the process of fundamental measurement. It is a prerequisite that our data fit the model sufficiently in order to achieve invariant interval-level measurement. Indeed, the benefits and attractive properties of Rasch measurement exist only to the extent that the data fit the model’s demanding requirements. This is consistent with the position emphasized throughout this text: Even in the most complex measurement situations, individual attributes should be measured one at a time.