Boosting to control programming of non-volatile memory

A system is disclosed for programming non-volatile memory with greater precision. In one embodiment, the system includes applying a first phase of a boosting signal to one or more unselected word lines for a set of NAND strings, applying a programming level to selected bit lines of the NAND strings while applying the first phase of the boosting signal, and applying an inhibit level to unselected bit lines of the NAND strings while applying the first phase of the boosting signal. Subsequently, a second phase of the boosting signal is applied to the one or more unselected word lines and the signal(s) on the selected bit lines are changed by applying the inhibit level to the selected bit lines so that NAND strings associated with the selected bit lines will be boosted by the second phase of the boosting signal. A program voltage signal is applied to a selected word line in order to program storage elements connected to the selected word line.