Techniques are provided for pre-charging NAND strings during a programming operation. The NAND strings are in a block that is divided into vertical sub-blocks. During a pre-charge phase of a programming operation, an overdrive voltage is applied to some memory cells and a bypass voltage is applied to other memory cells. The overdrive voltage allows the channel of an unselected NAND string to adequately charge during the pre-charge phase. Adequate charging of the channel helps the channel voltage to boost to a sufficient level to inhibit programming of an unselected memory cell during a program phase. Thus, program disturb is prevented, or at least reduced. The technique allows, for example, programming of memory cells in a middle vertical sub-block without causing program disturb of memory cells that are not to receive programming.