  It has been proposed that there are two types of superconductivity in
CeCu2Si2, mediated by spin fluctuations at ambient pressure, and by critical
valence fluctuations around a charge instability at a pressure P_v \simeq 4.5
GPa. We present in detail some of the unusual features of this novel type of
superconducting state, including the coexistence of superconductivity and huge
residual resistivity of the order of the Ioffe-Regel limit, large and pressure
dependent resistive transition widths in a single crystal measured under
hydrostatic conditions, asymmetric pressure dependence of the specific heat
jump shape, unrelated to the resistivity width, and negative temperature
dependence of the normal state resistivity below 10 K at very high pressure.
