The purpose of this study is to determine an efficient way to reduce the bias in estimates of the Rasch model parameters due to aberrant response patterns. First, the benefits of using one- or two-sided goodness-of-fit tests of patterns with the model are discussed. Then, the consequences of removing non-fitting patterns from Rasch model data are considered. Finally, an iterative procedure to reduce the bias is presented. This procedure replaces non-fitting patterns by certain patterns sampled according to the model. The effectiveness of this procedure is investigated in a simulation study using Rasch model data mixed with aberrant response data. It is also demonstrated that, for aberrant response behavior that too often results in ideal patterns, another strategy for detecting aberrant patterns is needed. Such a strategy would provide a possibility to detect more types of aberrant behavior and to reduce bias in the estimates of the model parameters. Four data tables and seven graphs are included. (Author/TJH)