O-minimal structures have quite nice properties, for example the existence of a cell decomposition. This is why we try to expand o-minimal structures, for example the definable sets in the ordered real field. The Paffian Closure is a possible way to do this. There we intersect the sets of the original o-minimal structure with Rolle leaves, which are special manifolds. To prove that the Paffian Closure of an o-minimal structure is again an o-minimal structure, we use a new version of Wilkie's Theorem of the Complement. Therefore we take the Charbonnel Closure of an o-minimal weak structure (which is similar to an o-minimal structure, but not closed under complementation). If every set is the projection of some zero sets of special functions, the theorem states that the Charbonnel Closure of the weak structure is again an o-minimal structure.