Screening of Coulomb interactions by itinerant deuterons contributes to the enhancement of the deuteron-deuteron reaction rate in some metal deutendes and fast deuteron conductors such as PdDx, DyNax WO3, SrCeO3: Y, Nb, and so forth. We propose that the deuteron screening mechanism also gives rise to the anomalous isotope effect in the PdD(H) system and to the increase in the superconducting transition temperature Tc of DxYBa2Cu3O7−δ. In conjunction with the currently known factors that govern superconductivity, the deuteron screening might lead to a new class of superconductors.