We analyze the complexity of reasoning with circumscribed low-complexity DLs such as DL-lite and the EL family, under suitable restrictions on the use of abnormality predicates. We prove that in circumscribed DL-lite<sub>R</sub> complexity drops from NExp<sup>NP</sup> to the second level of the polynomial hierarchy. In EL, reasoning remains ExpTime-hard, in general. However, by restricting the possible occurrences of existential restrictions, we obtain membership in Sigma<sup>p<sub>2</sub></sup> and Pi<sup>p<sub>2</sub></sup> for an extension of EL.

Piero A. Bonatti, Marco Faella, Luigi Sauro