Achieving high spatial resolution in contact sensing for robotic manipulation often comes at the price of increased complexity in fabrication and integration. One traditional approach is to fabricate a large number of taxels, each delivering an individual, isolated response to a stimulus. In contrast, we propose a method where the sensor simply consists of a continuous volume of piezoresistive elastomer with a number of electrodes embedded inside. We measure piezoresistive effects between all pairs of electrodes in the set, and count on this rich signal set containing the information needed to pinpoint contact location with high accuracy using regression algorithms. In our validation experiments, we demonstrate submillimeter median accuracy in locating contact on a 10mm by 16mm sensor using only four electrodes (creating six unique pairs). In addition to extracting more information from fewer wires, this approach lends itself to simple fabrication methods and makes no assumptions about the underlying geometry, simplifying future integration on robot fingers.