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One of the most criticized features of Bayesian statistics is the fact thatcredible intervals, especially when open likelihoods are involved, may stronglydepend on the prior shape and range. Many analyses involving open likelihoodsare affected by the eternal dilemma of choosing between linear and logarithmicprior, and in particular in the latter case the situation is worsened by thedependence on the prior range under consideration. In this letter, we revive asimple method to obtain constraints that depend neither on the prior shape norrange and, using the tools of Bayesian model comparison, extend it to overcomethe possible dependence of the bounds on the choice of free parameters in thenumerical analysis. An application to the case of cosmological bounds on thesum of the neutrino masses is discussed as an example.

Constraining power of open likelihoods, made prior-independent