Boosting signals are applied to unselected word lines for a set of NAND strings while a program voltage signal is applied to a selected word line. For a selected NAND string, in a first interval, the drain select gate is opened so that the NAND string communicates with a respective bit line to discharge channel boosting in the NAND string. In a second interval, the drain select gate is closed so that the NAND string is cutoff from the bit line, and the bit line voltage is raised from the level which allows discharging to an inhibit level. In a third interval, the drain select gate is opened again, and the inhibit level of the bit line slows programming. This approach avoids raising the NAND string to a respective starting condition which is based on a source follower action of the drain select gate.