In a NAND non-volatile memory system, a sensing process accounts for a relative position of a selected non-volatile storage element in a NAND string. In one approach, the storage elements are assigned to groups based on their position, and each group receives a common sensing adjustment during a verify or read process. A group which is closest to a source side of the NAND string may be the largest of all the groups, having at least twice as many storage elements as the other groups. The adjusting can include adjusting a sensing parameter such as body bias, source voltage, sensing time or sensing pre-charge level, based on the position of the sensed storage element or its associated word line position. The adjusting of the sensing may also be based on the control gate voltage and the associated data state involved in a specific sensing operation.