A network storage server restores a selected file or files from a block-level backup of a data set that contains multiple files, by using a client-server backup protocol, without restoring the entire data set. The backup can include at least one incremental backup image, in which case the file can be restored at least partially from the incremental backup image. A particular version of a file can also be restored, from a block-level backup image that includes multiple snapshots, by automatically selecting a particular snapshot associated with that version of the file, from the backup image, and using the selected snapshot to restore the file.