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Nowadays, saturation-based reasoners for the OWL EL profile of the Web Ontology Language are able to handle large ontologies such as SNOMED very efficiently. However, it is currently unclear how saturation-based reasoning procedures can be extended to very expressive Description Logics such as SROIQ--the logical underpinning of the current and second iteration of the Web Ontology Language. Tableau-based procedures, on the other hand, are not limited to specific Description Logic languages or OWL profiles, but even highly optimised tableau-based reasoners might not be efficient enough to handle large ontologies such as SNOMED. In this paper, we present an approach for tightly coupling tableau- and saturation-based procedures that we implement in the OWL DL reasoner Konclude. Our detailed evaluation shows that this combination significantly improves the reasoning performance for a wide range of ontologies.