Filtering snoop traffic in a multiprocessor computing system, each processor in the multiprocessor computing system coupled to a high level cache and a low level cache, the including: receiving a snoop message that identifies an address in shared memory targeted by a write operation; identifying a set in the high level cache that maps to the address in shared memory; determining whether the high level cache includes an entry associated with the address in shared memory; responsive to determining that the high level cache does not include an entry corresponding to the address in shared memory: determining whether the set in the high level cache has been bypassed by an entry in the low level cache; and responsive to determining that the set in the high level cache has not been bypassed by an entry in the low level cache, discarding the snoop message.