Technology for limiting a voltage difference between two selected conductive lines in a cross-point array when using a forced current approach is disclosed. In one aspect, the selected word line voltage is clamped to a voltage limit while driving an access current through a region of the selected word line and through a region of the selected bit line. The access current flows through the memory cell to allow a sufficient voltage to successfully read or write the memory cell, while not placing undue stress on the memory cell. In some aspects, the maximum voltage that is permitted on the selected word line depends on the location of the selected memory cell in the cross-point memory array. This allows memory cells for which there is a larger IR drop to receive an adequate voltage, while not over-stressing memory cells for which there is a smaller IR drop.