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 View the MathML sourcePv≃4.5GPa. 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