A technique for erasing non-volatile memory such as a NAND string which includes non-user data or dummy storage elements. The voltages of the non-user data storage elements are capacitively coupled higher by controlled increases in an erase voltage which is applied to a substrate. The voltages are floated by rendering a pass gate transistor in a non-conductive state, where the pass gate transistor is between a voltage driver and a non-user data storage element. Voltages of select gate transistors can also be capacitively coupled higher. The substrate voltage can be increased in steps and/or as a continuous ramp. In one approach, outer dummy storage elements are floated while inner dummy storage elements are driven. In another approach, both outer and inner dummy storage elements are floated. Write-erase endurance of the storage elements is increased due to reduced charge trapping between the select gates and the dummy storage elements.