The dispersion relation for a thin-skin pinch surrounded by a thick conducting liner and a superconducting wall is derived. The limits of the usual thin-liner approximation are discussed. It is shown that, depending on the ratio between the instability growth time and some characteristic diffusion times, three different regimes are found in which the growth rate is either independent of the liner thickness and the superconducting wall position or depends on the liner thickness only or, finally, on both parameters.