  Simultaneous resistivity and a.c.-specific heat measurements have been
performed under pressure on single crystalline CeCu2Si2 to over 6 GPa in a
hydrostatic helium pressure medium. A series of anomalies were observed around
the pressure coinciding with a maximum in the superconducting critical
temperature, $T_c^{max}$. These anomalies can be linked with an abrupt change
of the Ce valence, and suggest a second quantum critical point at a pressure
$P_v \simeq 4.5$ 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
$P_v$ in this picture, while other anomalies found around $P_v$ can be
qualitatively understood using the same model.
