The overall performance of a shared-memory, common bus multiprocesser system can be seriously affected by useless coherence-related actions. This occurs, in particular, when a private data block of a process becomes resident in more than one cache as a consequence of the migration of the owner process. We introduce a hardware solution to eliminate these useless shared copies, and show how this technique can be applied to a specific coherence protocol. Two extreme workload conditions are properly selected to evaluate the performance of a multiprocessor system.