The ionic polarizability of organic metals and of high-Tc cuprates is very high while the density of conduction electrons is low. As a result, the ionic polarizability screens out the electronic polarizability for states very close to the Fermi surface. The cut-off is determined by the dispersion of the ionic polarizability. The electron-phonon matrix element is very large for the ionically screened states, and is the cut-off for the electronically screened states. Therefore, the McMillan coupling constant λ p hi s v e r y l a r g e a t v e r y low energies, and has a low energy cut-off. This model accounts for both normal and superconducting state anomalies in organic metals, as well as cuprates.