Memory cells, memory systems and methods are described. In one embodiment, a memory cell includes electrodes and a memory element, and a first electrically conductive structure is formed within dielectric material providing the memory element in a low resistance state as a result of a first voltage of a first polarity being applied across the electrodes. Additionally, the first electrically conductive structure is removed from the dielectric material providing the memory element in a high resistance state as a result of a second voltage of a second polarity, which is opposite to the first polarity, being applied across the electrodes. A permanent and irreversible electrically conductive structure is formed within the dielectric material providing the memory element in the low resistance state as a result of a third voltage of the second polarity and having an increased potential compared with the second voltage being applied across the electrodes.