Conductivities of polymers, irradiated up to high doses, have been studied since two decades. We have expanded this knowledge to the low dose regime, where single non-overlapping in tracks are found. These tracks exhibit somethough very lowconductivity. When the conducting zones of these ion tracks overlap, the overall polymeric conductivity comes to saturation. Variations in conductivity parallel and transverse to the ion tracks are studied, and new hints for the underlying conductivity mechanism are summarized.