Ecological regression studies are widely used in geographical epidemiology to assess the relationships between health hazard and putative risk factors. Very often, health data are measured at an aggregate level because of confidentiality restrictions, while putative risk factors are measured on a different grid, i.e., independent (exposure) variable and response (counts) variable are spatially misaligned. To perform a regression of risk on exposure, one needs to realign the spatial support of the variables. Bayesian hierarchical models constitute a natural approach to the problem because of their ability to model the exposure field and the relationship between exposure and relative risk at different levels of the hierarchy, taking proper account of the variability induced by the covariate estimation. In the current paper, we propose two fully Bayesian solutions to the problem. The first one is based on the kernel-smoothing technique, while the second one is built on the tessellation of the study region. We illustrate our methods by assessing the relationship between exposure to uranium in drinkable waters and cancer incidence, in South Carolina (USA).