An electrically programmable non-volatile memory array and associated circuitry, including programming circuitry that adaptively senses completed programming of a selected memory cell. A programming bit line driver is connected to the bit line, and a first transistor has its source/drain path connected in series with the memory cell, and its gate connected to the output of the current comparator. As the MOS transistor in the selected cell becomes programmed, its drain current drawn from the bit line driver decays, and a remainder current into the current comparator increases. Upon the remainder current exceeding the reference current, the comparator turns off the first transistor; a second transistor connected between the source and drain of the cell transistor is turned on. In another approach, a summed current controls the gates of the first and second transistors. Programming terminates, and over-programming is avoided.