The poyion-ion preferential interaction coefficient F describes the exclusion of coions and accumulations of counterions in the vicinity of a polyion in an aqueous solution. We give tight upper and lower bounds for F when the polyion can be modeled by a cylinder of infinite length but of arbitrary charge density. This case can be used as a model for long strands of DNA or RNA in an aqueous solution containing univalent cations. The salt dependence of Gamma is predicted from low to intermediate and high salt concentrations. We also indicate how the bounds for the infinite polyion can be exploited to place bounds for polyions of length greater than a constant on the order of the inverse Debye screening length.