A method for data storage includes storing data in a group of analog memory cells by writing respective first storage values into the memory cells. After storing the data, respective second storage values are read from the memory cells. A subset of the memory cells, in which the respective second storage values have drifted below a minimum readable value, is identified. The memory cells in the subset are operated on, so as to cause the second storage values of at least one of the memory cells in the subset to exceed the minimum readable value. At least the modified second storage values are re-read so as to reconstruct the stored data.