The concept of strong admissibility plays an important role in some of the dialectical proof procedures that have been stated for grounded semantics. As the grounded extension is the (unique) biggest strongly admissible set, to show that an argument is in the grounded extension it suffices to show that it is in a strongly admissible set. We are interested in identifying a strongly admissible set that minimizes the number of steps needed in the associated dialectical proof procedure. In the current work, we look at the computational complexity of doing so.