The adequacy of several approaches to estimation of proficiency distributions for the Trial State Assessment (TSA) in eighth grade mathematics of the National Assessment of Educational Progress was examined. These approaches are more restrictive than the estimation procedures originally used, with the same kind of plausible-values approach that has been implemented since 1984 with the national assessment. The proposed approaches are computationally less burdensome and could provide improved performance from a statistical standpoint. Results from six procedures including the operational procedure for 1990 are compared to results obtained by a criterion procedure for eight TSA jurisdictions. With some modifications, alternatives were generated by crossing the method of obtaining principal components, the method of selecting principal components, and the procedure for estimating the model. Methods that estimate a single population model did not provide acceptable results. Results support use of the less restricted models, particularly the one used operationally in 1990, producing separate sets of principal components for each jurisdiction from each jurisdiction's within-state correlation matrix, with decisions about the components to include made separately for each jurisdiction on the basis of the percent-of-trace criterion applied to the jurisdiction's correlation matrix. A separate population model is then estimated for each jurisdiction. Fourteen tables, 2 appendices presenting data from the analyses, and a 20-item list of references are included. (SLD)