In default logic, possible sets of conclusions from a default theory are given in terms of extensions of that theory. Each such extension is generated through a set of defaults rules. In this paper, we are concerned with identifying default rules belonging to all sets of default rules generating different extensions. This is interesting from several perspectives. First, it allows for approximating the set of so-called skeptical conclusions of a default theory, that is, those conclusions belonging to all extensions. Second, it provides a technique usable for pre-processing default theories, because such default rules are applicable without knowing nor altering the extensions of the initial theory. The fact that our technique leaves the resulting conclusions unaffected makes it thus applicable as a universal pre-processing tool to all sorts of computational tasks.