  We consider dc-conductivity $\sigma$ of a mixture of small conducting and
insulating grains slightly below the percolation threshold, where finite
clusters of conducting grains are characterized by a wide spectrum of sizes.
The charge transport is controlled by tunneling of carriers between neighboring
conducting clusters via short ``links'' consisting of one insulating grain.
Upon lowering temperature small clusters (up to some $T$-dependent size) become
Coulomb blockaded, and are avoided, if possible, by relevant hopping paths. We
introduce a relevant percolational problem of next-nearest-neighbors (NNN)
conductivity with excluded small clusters and demonstrate (both numerically and
analytically) that $\sigma$ decreases as power law of the size of excluded
clusters. As a physical consequence, the conductivity is a power-law function
of temperature in a wide intermediate temperature range. We express the
corresponding index through known critical indices of the percolation theory
and confirm this relation numerically.
