A method for data storage includes accepting data for storage in a memory that includes multiple analog memory cells. The data is stored in a first group of the memory cells by programming a second group of the memory cells so as to cause the second group to generate interference in the first group, and individually erasing the first group while verifying that analog levels of the memory cells in the first group subject to the interference are within a predefined bound following erasure. After erasing the first group, the first group of the memory cells is programmed with the data.