Distinguishing features of metastable high-resistance states produced in GaSb by annealing a quenched high-pressure phase are a very low conductivity a which furthermore varies little with temperature (since h u m T"~) and an anomalous superconducting response below the superconducting-transition temperature T, (exponential decrease of the conductivity o). This aggregate of properties can be explained within the framework of a granulated-metal model with granules having a branched fractal surface. The large capacitance between these granules makes the Coulomb-energy changes in tunneling negligibly small, i.e., makes the tunneling non-activating.