Abstract In ontology-mediated querying with an expressive description logic (DL) L, two desirable properties of a TBox T are (1) being able to replace T with a TBox formulated in the Horn-fragment of L without affecting the answers to conjunctive queries (CQs) and (2) that every CQ can be evaluated in PT IME w.r.t. T . We investigate in which cases (1) and (2) are equivalent, finding that the answer depends on whether the unique name assumption (UNA) is made, on the DL under consideration, and on the nesting depth of quantifiers in the TBox. We also clarify the relation between query evaluation with and without UNA and consider natural variations of property (1).