Learning the structure of Bayesian Networks from data is a NP-Hard problem that involves an optimization task on a super-exponential sized space. In this work, we show that in most real life datasets, a number of the arcs contained in the final structure can be pre-screened at low computational cost with a limited impact on the global graph score. We formalize the identification of these arcs via the notion of quasi-determinism, and propose an algorithm exploiting the screening that reduces the structure learning on a subset of the original variables. We show, on diverse benchmark datasets, that this algorithm exhibits a significant decrease in computational time for little decrease in performance score.