Abstract: Markov chain Monte Carlo simulation techniques enable the ap plication of Bayesian methods to a variety of models where the posterior density of interest is too difficult to explore analytically. In practice, how ever, multivariate posterior densities often have characteristics which make implementation of MCMC methods more difficult. A number of techniques have been explored to help speed the convergence of a Markov chain. This paper presents a new algorithm which employs some of these techniques for cases where the target density is bounded. The algorithm is tested on sev eral known distributions to empirically examine convergence properties. It is then applied to a wildlife disease model to demonstrate real-world appli cability.