The problem of obtaining designs that result in the most precise parameter estimates is encountered in at least two situations where item response theory (IRT) models are used. In so-called two-stage testing procedures, certain designs that match difficulty levels of the test items with the ability of the examinees may be located. Such designs have the advantage that the variance of the estimated parameters can be controlled. In situations in which IRT models are applied to different groups, efficient multiple-matrix sampling designs are applicable. The choice of matrix sampling designs will also influence the variance of the estimated parameters. In this paper, heuristic arguments are given to formulate the efficiency of a design in terms of an asymptotic generalized variance criterion, and a comparison of the efficiencies of several designs is made. It is shown that some designs may be found to be most efficient for the one-parameter model and two-parameter model, but not necessarily so for the three-parameter model. Five figures are included. (Author)