There have been many attempts in recent years to map incidence and mortality from diseases such as cancer. Such maps usually display either relative rates in each district, as measured by a standardized mortality ratio (SMR) or some similar index, or the statistical significance level for a test of the difference between the rates in that district and elsewhere. Neither of these approaches is fully satisfactory and we propose a new approach using empirical Bayes estimation. The resulting estimators represent a weighted compromise between the SMR, the overall mean relative rate, and a local mean of the relative rate in nearby areas. The compromise solution depends on the reliability of each individual SMR and on estimates of the overall amount of dispersion of relative rates over different districts.