By using informational consistency requirements, Jaynes (1968) derives the form of maximal non-informative priors for regression coefficients, to be uniform. However, this result does not tell us what the limits of this uniform distribution should be. If we are faced with a problem of model selection this information is an integral part of the evidence, which is used to rank the various competing models. In this paper, we give some guidelines for choosing a parsimoneous proper uniform prior. It turns out that in order to construct such a parsimoneous prior one only needs to assign a maximal length to the dependent variable and minimal lengths to the independent variables, together with their maximal correlations.