Errors in knowledge bases (KBs) written in a Description Logic (DL) are usually detected when reasoning derives an inconsistency or a consequence that does not hold in the application domain modelled by the KB. Whereas classical repair approaches produce maximal subsets of the KB not implying the inconsistency or unwanted consequence, optimal repairs maximize the consequence sets. In this paper, we extend previous results on how to compute optimal repairs from the DL 𝓔𝓛 to its extension 𝓔𝓛⊥, which in contrast to 𝓔𝓛 can express inconsistency. The problem of how to deal with inconsistency in the context of optimal repairs was addressed previously, but in a setting where the (fixed) terminological part of the KB must satisfy a restriction on cyclic dependencies. Here, we consider a setting where this restriction is not required. We also show how the notion of optimal repairs obtained this way can be used in inconsistency- and error-tolerant reasoning.