Circumscription is a prominent approach to bring non-monotonicity to Description Logics (DLs), but unfortunately, it usually displays very high computational complexity of reasoning. Many works have studied circumscribed DLs, but most of them focus on expressive DLs containing ALC, and the results for low-complexity DLs are limited. This paper summarises some recent progress in characterizing the computational complexity of reasoning in circumscribed DL-Lite. We perform a two-dimensional analysis, considering different languages of the DL-Lite family, and varying how concepts and roles are treated. In addition to classical circumscription, we consider the recently studied pointwise circumscription, which shows better complexity, in some cases, and remains decidable in the presence of minimized roles.