Techniques are described for maintaining a pre-charge voltage in a NAND string in a program operation. After a pre-charge voltage is applied to the channel of a NAND string, the word line voltages are controlled to avoid a large channel gradient which generates electron-hole pairs, where the electrons can pull down the channel boosting level on the drain side of the selected word line. In one approach, the word line voltages of a group of one or more source side word lines adjacent to the selected word line are increased directly from the level used during pre-charge to a pass voltage. The word line voltages of other source side word lines, and of drain side word lines, can be decreased and then increased to the pass voltage to provide a large voltage swing which couples up the channel.