We give results of empirical Bayes (EB) estimation of mortality rates designed to smooth observed SMR when random fluctuation of the observed deaths is important. We have specially studied the case where the prior distributions of the EB method have a spatial structure. The need for spatial modelling of cancer mortality rates in France is first shown with testing autocorrelation and fitting autoregressive spatial models, conditional (CAR) or simultaneous (SAR). A positive autocorrelation of the rates is shown for most cancer sites studied. As expected, EB estimates of mortality rates for common tumours are similar to SMRs. For rare tumours, the EB method identifies the extreme rates more clearly than SMRs by smoothing the SMRs with large variances. CAR or SAR models are adequate prior distributions for autocorrelated rates and produce quite similar rate estimates.