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 detecting, in the instruction sequence, a barrier instruction that precedes the store instruction in program order and that includes a field set to indicate the store operation should be accorded 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.