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This article presents a simple procedure for obtaining demographic projections for small geographic areas. The method presented here is based on assuming that the trends of the areas to be projected will be similar to those observed in previous periods and taking the projections for larger geographic areas as a reference point. In mathematical terms, this technique involves a problem of restricted minimization of the quadratic divergences between the projections obtained and those observed in past periods, where the aggregate demographic projections are taken as a constraint. This proposal fits very well with the present scenario in the case of the demographic projections that the National Institute of Statistics prepares for Spain, where these forecasts are presented at a provincial level but not in any more detail. While these provincial projections are useful for policy planning and the provision of certain services by the public sector, it would be desirable to have them at a more detailed geographical scale at the provincial level. The procedure presented in this paper is illustrated with the case of five provinces in Spain, corresponding to the Autonomous Communities of Asturias and Galicia, in which the population forecasts for those provinces for the year 2033 are broken down to a parish geographical scale.