A method of programming memory cells (transistors) of a nonvolatile memory device from a first set of (previous) logic states to a second set of (final) logic states. The method includes applying program voltages to selected memory transistors; and applying a pre-verification voltage and a target verification voltage for verifying the current logic state of the selected memory transistors. The voltage interval between logic states of the second set of logic states is less than the voltage interval between logic states of the first set of logic states. A target verification voltage for verifying a first memory transistor is at one logic state of the second set is used as a pre-verification voltage for verifying that a second memory transistor to be programmed to higher logic state of the second set.