Computing smaller extracts of a larger ontology has been recognised as important for enabling tasks such as ontology creation, review, updating, debugging, navigation, sharing and integration. In addition, reasoning tasks such as querying and classification take less time to execute over a smaller extract than over the original ontology. We have developed new software to compute concise extracts of SNOMED CT that are semantically complete with respect to a set of input concepts, called ocus concepts. The two main criteria for these extracts, called subontologies, are: (i) Focus concepts must be defined equivalently in the subontology and the source ontology. (ii) The transitive closure (with respect to subsumption) between concepts occurring in the extract must be equal in the subontology and the source ontology, up to the signature of concepts in the subontology. The subontology extraction approach automatically identifies additional supporting concepts that are required to satisfy condition (i) and includes these in the extracted subontology.