A Monte Carlo study was conducted to examine the accuracy of differential item functioning (DIF) detection using the differential functioning of items and tests (DFIT) method. Specifically, the performance of DFIT was compared using "testwide" critical values suggested by Flowers, Oshima, and Raju, based on simulations involving large numbers of DIF-free items, with item-specific critical values obtained via the newer item parameter replication (IPR) method. Also examined were the benefits of single-stage, two-stage, and iterative linking for dichotomous and ordered polytomous data involving samples of various size, tests of different length, types and percentages of DIF items, and levels of impact. Overall, the results indicated that testwide and IPR-based critical values corresponding to a nominal alpha of .01 provided similar power for detecting DIF due to shifts in extremity parameters, but IPR power was generally lower when DIF was due to differences in discrimination. In addition, IPR-based critical values provided as good as or better control of Type I error under most conditions, and results improved for all methods when using two-stage and iterative linking rather than single-stage linking and DIF analysis. The implications of these findings for future research involving the DFIT method with various item response models are discussed. (Contains 7 tables.)