Unselected groups of non-volatile storage elements are boosted during programming to reduce or eliminate program disturb for targeted, but unselected memory cells connected to a selected word line. Prior to applying a program voltage to the selected word line and boosting the unselected groups, the unselected groups are pre-charged to further reduce or eliminate program disturb by providing a larger boosted potential for the unselected groups. During pre-charging, one or more pre-charge enable signals are provided at higher voltages for certain memory cells that may have undergone partial programming.