  Massive gravity models in 2+1 dimensions, such as those obtained by adding to
Einstein's gravity the usual Fierz-Pauli, or the more complicated Ricci scalar
squared ($R^2$), terms, are tree level unitary. Interesting enough these
seemingly harmless systems have their unitarity spoiled when they are augmented
by a Chern-Simons term. Furthermore, if the massive topological term is added
to $R + R_{\mu\nu}^2$ gravity, or to $R + R_{\mu\nu}^2 + R^2$ gravity
(higher-derivative gravity), which are nonunitary at the tree level, the
resulting models remain nonunitary. Therefore, unlike the common belief, as
well as the claims in the literature, the coexistence between three-dimensional
massive gravity models and massive topological terms is conflicting.
