The most commonly used item response theory models are those assuming a unidimensional latent trait (d=1), monotone item response functions (M), and local independence (LI). If these assumptions are violated the data is typically either modeled incorrectly or by assuming a multidimensional latent trait (d>1), M, and LI. The use of a d>1 trait is not always desirable however. In many cases there is a single dimension of interest, with the remainder being nuisance dimensions. In this case the primary goal is often to estimate the loss of information when a d=1 model is used incorrectly. Another reason that d>1 may be undesirable is that many of the statistical tests of d=1, M, LI are based on conditioning on a unidimensional latent trait and measuring the departure from LI. The d>1 models thus do not directly relate to the commonly used measures of departure from d=1, M, LI. Recently, these issues have been addressed by Ip (1998) and Pashley and Reese (in press). We examine their procedures and discuss two weaknesses in their approaches: inability to model guessing, and failure to examine which of the underlying correlation matrices are possible. A proposal for dealing with these difficulties is made, and some of the remaining issues in doing so are discussed. Joint work with Louis Roussos, Law School Admission Council.