Abduction is the task of finding possible extensions of a given knowledge base that would make a given sentence logically entailed. As such, it can be used to explain why the sentence does not follow, to repair incomplete knowledge bases, and to provide possible explanations for unexpected observations. We consider TBox abduction in the lightweight description logic EL, where the observation is a concept inclusion and the background knowledge is a description logic TBox. To avoid useless answers, such problems usually come with further restrictions on the solution space and/or minimality criteria that help sort the chaff from the grain. We argue that existing minimality notions are insufficient, and introduce connection minimality. This criterion rejects hypotheses that use concept inclusions “disconnected” from the problem at hand. We show how to compute a special class of connection-minimal hypotheses in a sound and complete way. Our technique is based on a translation to first-order logic, and constructs hypotheses based on prime implicates. We evaluate a prototype implementation of our approach on ontologies from the medical domain.