Information stored as physical states of cells of a memory is read by setting each of one or more references to a respective member of a first set of values and reading the physical states of the cells according to the first set. Then, at least some of the references are set to respective members of a second set of values, and the physical states of the cells are read according to the second set. At least one member of the second set is different from any member of the first set, so that the two readings together read the physical states of the cells with higher resolution than the first reading alone.