Standard approaches for estimating item response theory (IRT) model parameters generally work under the assumption that the latent trait being measured by a set of items follows the normal distribution. Estimation of IRT parameters in the presence of nonnormal latent traits has been shown to generate biased person and item parameter estimates. A number of methods, including Ramsay curve item response theory, have been developed to reduce such bias, and have been shown to work well for relatively large samples and long assessments. An alternative approach to the nonnormal latent trait and IRT parameter estimation problem, nonparametric Bayesian estimation approach, has recently been introduced into the literature. Very early work with this method has shown that it could be an excellent option for use when fitting the Rasch model when assumptions cannot be made about the distribution of the model parameters. The current simulation study was designed to extend research in this area by expanding the simulation conditions under which it is examined and to compare the nonparametric Bayesian estimation approach to the Ramsay curve item response theory, marginal maximum likelihood, maximum a posteriori, and the Bayesian Markov chain Monte Carlo estimation method. Results of the current study support that the nonparametric Bayesian estimation approach may be a preferred option when fitting a Rasch model in the presence of nonnormal latent traits and item difficulties, as it proved to be most accurate in virtually all scenarios that were simulated in this study.