Forgetting is an important ontology extraction technique. A variant of forgetting which has received significant attention in the literature is \emph{deductive forgetting}. While \emph{deductive forgetting} is attractive as it generates the forgetting view in a language with the same complexity as the language of the original ontology, it is known to be not precise as it may not preserve the information that requires more complex languages. We study \emph{deductive forgetting} with the aim of understanding the unpreserved information. We present a system that performs \emph{deductive forgetting} and produces a set of axioms~$\Delta$ representing the unpreserved information in the forgetting view. Our system allows a new fine-grained ontology extraction process that gives the user the option to enhance the informativeness of the deductive forgetting view by appending to it axioms from~$\Delta$.