In item response theory (IRT), preequating depends upon item parameter estimate invariance. Three separate simulations, all using the unidimensional three-parameter logistic item response model, were conducted to study the impact of the following variables on preequating: (1) mean differences in ability; (2) multidimensionality in the data; and (3) a combination of mean differences in ability and multidimensionality. One of the Scholastic Aptitude Test mathematical forms (3ASA3) which provided the least acceptable preequating was selected to define true item and person parameters for these simulations. A random sample of 2,744 examinees was used. The LOGIST computer program was chosen to estimate item parameters for the 60 items in 3ASA3 and the 24 items in the equating section fn. Results showed that differences in mean true ability can cause differences in the precision with which a particular estimation procedure estimates parameters. The introduction of a particular kind of multidimensionality in the data can have a large impact on estimation precision when the IRT model is unidimensional. The combination of a slight decrease in mean ability and a particular type of multidimensionality in the data also has a large impact on estimation precision when the IRT model is unidimensional, although the impact is lessened somewhat. (JAZ)