A method for data storage in analog memory cells includes defining multiple programming states for storing data in the analog memory cells. The programming states represent respective combinations of more than one bit and correspond to respective, different levels of a physical quantity stored in the memory cells. The data is stored in the memory cells by applying to the memory cells programming pulses that cause the levels of the physical quantity stored in the memory cells to transition between the programming states, such that a given transition is caused by only a single programming pulse.