A technique for erasing a non-volatile memory applies a p-well voltage to a substrate and drives or floats select gate voltages to accurately control the select gate voltage to improve write-erase endurance. Source and drain side select gates of a NAND string are driven at levels to optimize endurance. In one approach, the select gates float after being driven at a specific initial level, to reach a specific, optimal final level. In another approach, the select gates are driven at specific levels throughout an erase operation, in concert with the p-well voltage. In another approach, onset of select gate floating is delayed while the p-well voltage ramps up. In another approach, p-well voltage is ramped up in two steps, and the select gates are not floated until the second ramp begins. Floating can be achieved by raising the drive voltage to cut off pass gates of the select gates.