Carbon-filled polyethylene composites were fabricated and tested to establish the practical lower limit of their electrical resistivity at room temperature and to investigate the trade-offs between low resistivity and the magnitude of the resistance anomaly (i.e., a large positive temperature coefficient of resistivity) that appears when such composites are heated through the polyethylene crystalline melting transition. Carbon blacks with large particle size and low surface area provided low-resistivity composites having large resistance anomalies. The largest resistance anomalies were found in composites that were well mixed, but the room-temperature resistivity also increased in composites that were cycled repetitively through the crystalline-melting transition. A mixture of carbon blacks of two different sizes provided a lower resistance than was found in a material with the same fill of only the coarser black. By controlling the composition and the processing, composites were made with room-temperature resistivities lower than 0.2 ohm cm and resistance changes of at least 2 orders of magnitude. A resistance change of as much as 5 orders of magnitude was obtained for composites with room-temperature resistivities of only 1 ohm cm.