We found no notable difference in performance between the BYM model, which uses a Gaussian distribution, and the L1 BYM version, which uses a heavier-tailed, double-exponential distribution. This finding is in agreement with that of an earlier simulation study (Best et al. 1999) that compared these two models. However, there were some clear differences between the BYM models and the spatial allocation model MIX. The performance of the latter model is characterized by an all-or-none feature in the sense that it tends to allocate the true raised-risk areas to either an elevated risk group or to a background group, depending on how much uncertainty is present in the data. If the information from the data is sufficient (i.e., moderate-size expected counts and/or high true excess risks) the MIX model is able to separate the raised-risk and background areas quite well, producing considerably less smoothing of the raised-risk estimates than BYM. When the information in the data is sparse, uncertainty in the groupings leads to more smoothing than the BYM. This type of dichotomy makes any decision rule exploiting the posterior distribution of the relative risks hard to calibrate and less useful than for the BYM model. The MIX model is best used for providing estimates of the underlying magnitude of the relative risks if those are clearly raised rather than as a tool for detecting the presence of areas with excess risk in a decision rule context.