Three methods of estimating test score distributions that may improve on using the observed frequencies (OBFs) as estimates of a population test score distribution are considered: the kernel method (KM); the polynomial method (PM); and the four-parameter beta binomial method (FPBBM). The assumption each method makes about the smoothness of the true distribution and computational details of the methods are described. The methods are compared in a simulation study in which 500 samples of size 500, 1,000, 2,000, and 5,000 are taken from three population distributions. For each of the 6,000 samples (3 population distributions by 4 sample sizes by 500 samples), the variable kernel, fixed kernel, FPBBM, and PM estimates of the true distribution are computed. The three population distributions are defined using observed raw score distributions on three tests for which a large number of examinees is available. Methods based on smoothness assumptions performed better than using the OBFs, and differences among the methods' performance were small compared to differences between the performance of the worst method and use of OBFs. The FPBBM performed best across all conditions, although the PM performed as well as the FPBBM for sample sizes of 5,000. The PM generally performed better than the KM except for one population for which the test score distribution was relatively flat. Four tables, 15 graphs, and a 13-item list of references are included. (Author/SLD)