Lean kernels (LKs) are an effective optimization for deriving the causes of unsatisfiability of a propositional formula. Interestingly, no analogous notion exists for explaining consequences of description logic (DL) ontologies. We introduce LKs for DLs using a general notion of consequence-based methods, and provide an algorithm for computing them which incurs in only a linear time overhead. As an example, we instantiate our framework to the DL ALCALC. We prove formally and empirically that LKs provide a tighter approximation of the set of relevant axioms for a consequence than syntactic locality-based modules.