Mapping of mortality rates has been a valuable public health tool. We describe novel Bayesian methods for constructing maps which do not depend on a post stratification of the estimated rates. We also construct posterior modal maps rather than posterior mean maps. Our methods are illustrated using mortality data from chronic obstructive pulmonary diseases (COPD) in the continental United States. Poisson regression models have attracted much attention in the scientific community for their superiority in modeling rare events (including mortality counts from COPD). Christiansen and Morris (JASA 1997) described a hierarchical Bayesian model for heterogeneous Poisson counts under the exchangeability assumption. We extend this model to include latent classes (groups of similar Poisson rates unknown to an investigator). Also, it is standard practice to construct maps using quantiles (e.g., quintiles) of the estimated mortality rates. For example, based on quintiles, the mortality rates are cut into 5 equal size groups, each containing $20\%$ of the data, and a different color is applied to each of them on the map. A potential problem is that, this method assumes an equal number of data in each group, but this is often not the case. The latent class model produces a method to construct maps without using quantiles, providing a more natural representation of the colors. Typically, for rare events, the posterior densities of the rates are skewed, making the posterior mean map inappropriate and inaccurate. Thus, although it is standard practice to present the posterior mean maps, we also develop a method to provide the joint posterior modal map (i.e., the map with the highest posterior probability over the ensemble). For the COPD data, collected 1988-1992 over 798 health service areas, we use Markov chain Monte Carlo methods to fit the model, and an output analysis is used to construct the new maps.