Hybrid Transactional Memory (TM) uses available hardware TM resources to execute language-level transactions, and falls back to a software TM implementation for those transactions that cannot complete in hardware. Ideally, a hybrid TM would allow hardware and software transactions to run concurrently, but would not waste hardware TM resources on coordination between the two classes of transactions. In addition, it should scale well, incur little latency, offer strong safety guarantees, and provide some degree of fairness. We introduce a new hybrid TM algorithm, “Hybrid Cohorts”, in which hardware transactions do not modify global metadata, and software transactions have ex- tremely low per-access overhead. The tradeoff is that hardware transactions cannot commit while software transactions are in flight. Evaluation on an 8-thread Intel Haswell CPU shows competitive performance with the current state-of-the-art. Furthermore, it does so while providing acceptable levels of fairness and safety, and offering opportunities for hardware acceleration.