1. A method of performing a copy operation, the method comprising: accessing with computer hardware a deduplication signature table containing a plurality of signatures corresponding to data blocks stored in at least one first storage device; using the deduplication signature table, performing, with computer hardware, a first deduplicated copy operation of a plurality of files from at least one second storage device to the first storage device thereby creating a deduplicated copy of the plurality of files in the first storage device; and with computer hardware and as part of a second deduplicated copy operation in which at least a subset of the plurality of data blocks which form the deduplicated copy are copied from the first storage device to at least one third storage device, for each respective data block in the subset: accessing from the first storage device a previously stored signature corresponding to the respective data block and which is stored separately from the deduplication signature table, the previously stored signature included in a first signature/data word of a plurality of signature/data words which is associated with the respective data block and is embedded in a file that includes others of the plurality of signature/data words associated with other data blocks in the subset, wherein first signature/data words of the plurality of signature/data words each include a respective signature and a respective actual data block copy stored physically or logically contiguously with respect to one another, and wherein second signature/data words of the plurality of signature/data words each include a respective signature and a respective reference to an actual data block copy stored physically or logically contiguously with respect to one another; transmitting the previously stored signature to the third storage device, wherein the previously stored signature is transmitted to the third storage device without re-generating the value of the previously stored signature using the respective data block; receiving a message indicating whether a copy of the respective data block is already stored on the third storage device; and if the message indicates that the respective data block is not already stored on the third storage device: accessing the respective data block from the first storage device; and transmitting the respective data block to the third storage device.