A select gate structure for a non-volatile storage system includes a select gate and a coupling electrode which are independently drivable. The coupling electrode is adjacent to a word line in a NAND string and has a voltage applied which reduces gate induced drain lowering (GIDL) program disturb of an adjacent unselected non-volatile storage element. In particular, an elevated voltage can be applied to the coupling electrode when the adjacent word line is used for programming. A reduced voltage is applied when a non-adjacent word line is used for programming. The voltage can also be set based on other programming criterion. The select gate is provided by a first conductive region while the coupling electrode is provided by a second conductive region formed over, and isolated from, the first conductive region.