In a method of multiple-bit programming of a three-dimensional memory device having arrays of memory cells that extend in horizontal and vertical directions relative to a substrate, the method comprises first programming a memory cell to be programmed to one among a first set of states. At least one neighboring memory cell that neighbors the memory cell to be programmed to one among the first set of states is then first programmed. Following the first programming of the at least one neighboring memory cell, second programming the memory cell to be programmed to one among a second set of states, wherein the second set of states has a number of states that is greater than the number of states in the first set of states.