Today's hardware transactional memory (HTM) systems rely on existing coherence protocols, which implement a requester-wins strategy. This, in turn, leads to poor performance when transactions frequently conflict, causing them to resort to a non-speculative fallback path. Often, such a path severely limits parallelism. In this article, we propose very simple architectural changes to the existing requester-wins HTM implementations that enhance conflict resolution between hardware transactions and thus improve their parallelism. Our idea is compatible with existing HTM systems, requires no changes to target applications that employ traditional lock synchronization, and is shown to provide robust performance benefits. CCS Concepts: • Computer systems organization → Multicore architectures; • Theory of computation → Parallel computing models;