A system for controlling contention between conflicting transactions in a transactional memory system. During operation, the system receives a request to access a cache line and then determines if the cache line is already in use by an existing transaction in a cache state that is incompatible with the request. If so, the system determines if the request is from a processor which is in a polite mode. If this is true, the system denies the request to access the cache line and continues executing the existing transaction.