A non-volatile memory device and method for programming cells using repeated pulses of program voltages, with interleaved read operations to determine the level of read current, until the desired programming state is achieved. Each successive program pulse has one or more program voltages increased by a step value relative to the previous pulse. For a single level cell type, each cell is individually removed from the programming pulses after reaching a first read current threshold, and the step value is increased for one or more kicker pulses thereafter. For a multi-level cell type, the step value drops after one of the cells reaches a first read current threshold, some cells are individually removed from the programming pulses after reaching a second read current threshold while others are individually removed from the programming pulses after reaching a third read current threshold.