Let us stress that we are not placing ourselves in the context of cluster detection methods based on so-called point data, that is, data where the precise geographic location of all the cases (and controls) is known. These methods, which have been reviewed in a number of monographs or special issues (e.g., Alexander and Boyle 1996) are typically used on a localized scale, mostly to study the spatial distribution of cases around a point source or different patterns of randomness or clustering of the cases in relation to those of controls. Here we are concerned with methods for describing the overall spatial pattern of cases aggregated over small areas and the interpretation of the residual variations once the Poisson noise has been smoothed out by the disease-mapping models. Several simulation exercises to study different aspects of the performance of disease-mapping models have been reported recently. For example, Lawson et al. (2000) compared a number of models that could be used for disease mapping by goodness of fit criteria that included correlation between the simulated map and the smoothed map and a Bayesian information criterion. They concluded that the version of the CAR model proposed by Besag et al. (1991) [Besag, Yorke, and Mollié (BYM) model] was the most robust model among those with spatial structure. We also consider the BYM model here and compare its performance with two models not considered by Lawson et al. (2000): a version of the BYM model that is more robust to outliers and hence may be better able to detect abrupt changes in the spatial pattern of risk, and a spatial mixture model proposed by Green and Richardson (2002) (see the section on Bayesian disease-mapping models for details). Our study also specifically addresses the smoothing of high-risk areas and further use of the posterior distribution of the relative risks for detecting areas with excess risk—issues not considered by Lawson et al. (2000). Jarup et al. (2002) reported the results of a small simulation study similar to ours; we chose the same study area and expected counts to carry out our comprehensive exercise.