A method for data storage includes encoding data with an inter-device Error Correction Code (ECC), and sending the encoded data for storage on two or more storage devices. The data to be stored on each of the storage devices, and which has been encoded with the inter-device ECC, is encoded with an intra-device ECC, and the data encoded with the inter-device and intra-device ECCs is stored on the storage device. After storing the data, at least part of the stored data is retrieved and output by decoding the intra-device and inter-device ECCs, while using information related to one of the intra-device and inter-device ECCs in decoding the other of the intra-device and inter-device ECCs.