Loop Thread-Level Speculation on Hardware Transactional Memories is a promising strategy to improve application performance in the multicore era. However, the reuse of shared scalar or array variables introduces constraints (false dependences or false sharing) that obstruct efficient speculative parallelization. Speculative privatization relieves these constraints by creating speculatively private data copies for each transaction thus enabling scalable parallelization. To support it, this paper proposes two new OpenMP clauses to parallel for that enable speculative privatization of scalar or arrays in may DOACROSS loops: spec_private and spec_reduction. We also present an evaluation that reveals that, for certain loops, speed-ups of up to 3.24 × can be obtained by applying speculative privatization in TLS.