Estimating super-structures (SS) as structural constraints for learning Bayesian networks (BN) is an important step of scaling up these models to high-dimensional problems. However, the literature has shown a lack of algorithms with an appropriate accuracy for such purpose. The recent Hybrid Parents and Children - HPC (De Morais and Aussem, 2010) has shown an interesting accuracy, but its local design and high computational cost discourage its use as SS estimator. We present here the OptHPC, an optimized version of HPC that implements several optimizations to get an efficient global method for learning SS. We demonstrate through several experiments that OptHPC estimates SS with the same accuracy than HPC in about 30% of the statistical tests used by it. Also, OptHPC showed the most favorable balance sensitivity/specificity and computational cost for use as super-structure estimator when compared to several state-of-the-art methods.