1. A method of performing a copy operation, the method comprising: copying, with one or more processors comprising computer hardware, a plurality of files from primary storage to one or more first secondary storage devices, wherein the files are formed from a plurality of source data blocks, wherein said copying is performed in a deduplicated manner and at least partly by: accessing a deduplication signature table containing a plurality of signatures which correspond to a plurality of backed up data blocks stored in the one or more first secondary storage devices; and storing, on the one or more first secondary storage devices, instances of ones of the plurality of source data blocks for which matching backed up data blocks do not already exist on the one or more first secondary storage devices; in response to instructions to copy at least some of the plurality of backed up data blocks from the one or more first secondary storage devices to one or more second secondary storage devices, for each respective data block of the at least some of the plurality of backed up data blocks: reading, with one or more processors comprising computer hardware, a previously stored signature corresponding to the respective data block for sending from the one or more first secondary storage devices to the one or more second secondary storage devices, wherein the previously stored signature is stored on the one or more first secondary storage devices and is separate from the deduplication signature table; and based on an indication as to whether the respective data block is already stored on the one or more second secondary storage devices, reading the respective data block from the one or more first secondary storage devices for sending to the one or more second secondary storage devices if the respective data block does not exist on the one or more second secondary storage devices, wherein the signature corresponding to the respective data block and not the respective data block itself is read from the one or more first secondary storage devices if the respective data block exists on the one or more second secondary storage devices.