One or more programming operations are performed on a set of non-volatile storage elements. For example, the programming operations may include applying a set of programming pulses. A verify process is performed to determine which of the non-volatile storage element have reached an intermediate verify threshold but have not reached a final verify threshold. One additional programming operation at a reduced level is performed for the non-volatile storage elements that have reached the intermediate verify threshold but have not reached the final verify threshold, and those non-volatile storage elements are then inhibited from further programming. Non-volatile storage elements that have not reached the intermediate verify threshold continue programming. Non-volatile storage elements that reach the final verify threshold are inhibited from programming.