In at least some embodiments, a processor core generates a store operation by executing a store instruction in an instruction sequence. The store operation is marked as a high priority store operation in response to the store instruction being marked as high priority and is not so marked otherwise. The store operation is buffered in a store queue associated with a cache memory of the processor core. Handling of the store operation in the store queue is expedited in response to the store operation being marked as a high priority store operation and not expedited otherwise.