A method for data storage includes storing data in a group of analog memory cells by writing respective storage values into the memory cells in the group. One or more of the memory cells in the group are read using a first readout operation that senses the memory cells with a first sense time. At least one of the memory cells in the group is read using a second readout operation that senses the memory cells with a second sense time, longer than the first sense time. The data stored in the group of memory cells is reconstructed based on readout results of the first and second readout operations.