A transactional memory (TM) includes a control circuit pipeline and an associated memory unit. The memory unit stores a plurality of rings. The pipeline maintains, for each ring, a head pointer and a tail pointer. A ring operation stage of the pipeline maintains the pointers as values are put onto and are taken off the rings. A put command causes the TM to put a value into a ring, provided the ring is not full. A get command causes the TM to take a value off a ring, provided the ring is not empty. A put with low priority command causes the TM to put a value into a ring, provided the ring has at least a predetermined amount of free buffer space. A get from a set of rings command causes the TM to get a value from the highest priority non-empty ring (of a specified set of rings).