Software-based, thread-level speculation (TLS) is a software technique that optimistically executes in parallel loops whose fully-parallel semantics can not be guaranteed at compile time. Modern TLS libraries allow to handle arbitrary data structures speculatively. This desired feature comes at the high cost of local store and/or remote recovery times: The easier the local store, the harder the remote recovery. Unfortunately, both times are on the critical path of any TLS system. In this paper we propose a solution that performs local store in constant time, while recover values in a time that is in the order of , being the number of threads. As we will see, this solution, together with some additional improvements, makes the difference between slowdowns and noticeable speedups in the speculative parallelization of non-synthetic, pointer-based applications on a real system. Our experimental results show a gain of 3.58 to 28 with respect to the baseline system, and a relative efficiency of up to, on average, 65 % with respect to a TLS implementation specifically tailored to the benchmarks used.