The gain in the Identification Capacity afforded by a rate-limited description of the noise sequence corrupting a modulo-additive noise channel is studied. Both the classical Ahlswede-Dueck version and the Ahlswede-Cai-Ning-Zhang version, which does not allow for missed identifications, are studied. Irrespective of whether the help is provided to the transmitter, to the receiver, or to both—the two capacities coincide and both equal the helper-assisted Shannon capacity.