Memory systems and memory programming methods are described. In one arrangement, a memory system includes a memory cell configured to have a plurality of different memory states, an access circuit coupled with the memory cell and configured to provide a first signal to a memory element of the memory cell to program the memory cell from a first memory state to a second memory state, and a current source coupled with the memory cell and configured to generate a second signal which is provided to the memory element of the memory cell after the first signal to complete programming of the memory cell from the first memory state to the second memory state.