This Monte Carlo study compares the ability of the parametric bootstrap version of DIMTEST with three goodness-of-fit tests calculated from a fitted NOHARM model to detect violations of the assumption of unidimensionality in testing data. The effectiveness of the procedures was evaluated for different numbers of items, numbers of examinees, correlations between underlying ability dimensions, skewness of underlying ability distributions, and the presence or absence of a guessing parameter. In the absence of guessing, DIMTEST and the NOHARM-based statistics had similar power, with the X[squared] statistic having a very low Type I error rate. In the presence of guessing, however, two of the NOHARM-based statistics had unacceptably high Type I error rates, while the third performed similarly to DIMTEST. Given this inflated error rate, the study compares the empirical powers after adjusting for the discrepancy in Type I error rates. (Contains 5 tables.)