Reiter's Default Logic is one of the most popular formalisms for describing default reasoning. One important defect of Default Logic is, however, the inability to reason by cases. Over the years, several solutions for this problem have been proposed. All these proposals deal with deriving new propositions through reasoning by cases. None, however, discuss the propositions that should no longer be derivable as a result of reasoning by cases. This paper discusses the latter subject. It shows that an intuitively plausible way of dealing with propositions that should no longer be derivable as a result of reasoning by cases, can have far reaching consequences. One of the consequences is that disjunctions must be viewed as describing possible extensions.