In the present paper a new shrinkage estimator of relative risk, useful in disease mapping, is compared with the empirical and full Bayes estimators, using death certificate data for lung cancer (males and females) and breast cancer (females) 1982-1988 in the Emilia-Romagna region (Italy). The estimates are obtained averaging the relative risks obtained from recursive partitioning of the set of observed values. The number of partitions is fixed in advance and behaves as a smoothing parameter, the lower the number the higher the degree of shrinkage toward the overall mean of the observed values.