Current industry proposals for hardware transactional memory focus on best-effort solutions where hardware limits are imposed on transactions. These designs can efficiently execute transactions but they may abort due to different hardware and operating system limitations, with a significant impact on performance. For instance, transactions cannot survive capacity overflows, exceptions, interrupts, operating system events like page faults, migrations, context switches, and so on. To deal with these events, best-effort hardware transactional memory systems usually provide a software fallback path to execute a non-transactional version of the code. In this paper we propose hardware implementation solutions to make transactions survive some of such limitations, in order to improve the performance and scalability of transactional applications in best-effort systems. First, we propose a hardware irrevocability mechanism that works either when hardware capacity overflows occur or in high contention scenarios. It anticipates capacity overflows and reduces the abort count. This mechanism avoids writing a fallback code, simplifying the programming of the transactional application. Second, we propose a two-phase abort mechanism to support both the execution of privileged mode code inside transactions and the interaction of this code with the irrevocability mechanism. Third, we propose a privileged-aware cache replacement policy to reduce capacity overflows in the presence of privileged code. We evaluate our proposals with all the benchmarks of the STAMP transactional suite and carry out a performance comparison with a fallback-based hardware transactional memory system, after considering different fallback codes, showing significant performance benefits for requester-wins and requester-stalls conflict resolution policies.