Simultaneous resistivity and ac specific heat measurements have been performed under pressure on singlecrystalline CeCu2Si2 to over 6 GPa in a hydrostatic helium pressure medium. A series of anomalies was observed around the pressure coinciding with a maximum in the superconducting critical temperature, Tc max . These anomalies can be linked with an abrupt change of the Ce valence and suggest a second quantum critical point at a pressure Pv.4.5 GPa, where critical valence fluctuations provide the superconducting pairing mechanism, as opposed to spin fluctuations at ambient pressure. Such a valence instability—and associated superconductivity—is predicted by an extended Anderson lattice model with Coulomb repulsion between the conduction and f electrons. We explain the T-linear resistivity found at Pv in this picture, while other anomalies found around Pv can be qualitatively understood using the same model