Read failure is reduced by increasing the drain current through a serial string of memory cells during the read operation. In one embodiment, this is accomplished by using a higher read pass voltage for unselected word lines when the selected word line is within a predetermined distance of the drain side of the memory block array. If the selected word line is closer to the source side, a lower read pass voltage is used. In another embodiment, the cells on the word lines closer to the drain side of the memory block array are erased to a lower threshold voltage than the memory cells on the remaining word lines.