Data blocks lost at a primary mass storage are restored while allowing the primary computer system to access the lost data block before full restoration. Restoration occurs along two channels. In the first channel, read requests issued by the primary computer system are handled by obtaining the requested data block from the backup mass storage device. The retrieved data block is then written to the primary mass storage, thereby restoring the primary mass storage for that data block. In the second channel of restoration, a snapshot copy of a selected data set of the backup mass storage is made and transported to the primary system. If the corresponding data block in the primary mass storage has a current data block, the data block is not written from the snapshot copy to the primary mass storage. Otherwise, the data block is copied from the snapshot copy to the primary mass storage.