Shifts in the apparent charge stored on a charge storing element of a non-volatile memory cell can occur because of the coupling of an electric field based on the charge stored in adjacent charge storing elements. To compensate for this coupling, the programming process for a given memory cell can take into account the target programmed state of one or more adjacent memory cell. The amount of programming is verified after each programming pulse and the standard verify level for the programming cell is dependent on the target state. The verify level is further offset lower dependent on the amount of perturbation from neighboring cells, determinable by their target states. The verify level is preferably virtually offset by biasing adjacent word lines instead of actually offsetting the standard verify level. For soft-programming erased cells, neighboring cells on both adjacent word lines are taken into account.