A non-volatile memory (NVM) system includes a set of NVM cells, each including: a NVM transistor; an access transistor coupling the NVM transistor to a corresponding bit line; and a source select transistor coupling the NVM transistor to a common source. The NVM cells are written by a two-phase operation that includes an erase phase and a program phase. A common set of bit line voltages are applied to the bit lines during both the erase and programming phases. The access transistors are turned on and the source select transistors are turned off during the erase and programming phases. A first control voltage is applied to the control gates of the NVM transistors during the erase phase, and a second control voltage is applied to the control gates of the NVM transistors during the program phase. Under these conditions, the average required number of Fowler-Nordheim tunneling operations is reduced.