1. A method of filtering snoop traffic in a multiprocessor computing system, each processor in the multiprocessor computing system coupled to a shared main memory, the method comprising: receiving, by a cache controller, a snoop message that identifies an address in the shared memory; determining, by the cache controller, that a high level cache does not include an entry associated with the address in the shared memory; determining, by the cache controller, whether a set in the high level cache that maps to the address in the shared memory has been bypassed by an entry in a low level cache; responsive to determining that the set in the high level cache has not been bypassed by an entry in the low level cache, discarding, by the cache controller, the snoop message; receiving, by the cache controller, an instruction to write data to the low level cache and to bypass the high level cache, wherein the instruction includes an address at which the data is stored in shared memory; writing, by the cache controller, the data into a cache line in the low level cache, wherein the cache line is selected in dependence upon the address at which the data is stored in shared memory; indicating, by the cache controller, that the data in the cache line of the low level cache bypasses the high level cache; identifying, by the cache controller, a set in the high level cache that maps to the address at which the data is stored in shared memory; and indicating, by the cache controller, that the set in the high level cache has been bypassed by an entry in the low level cache.