  We prove 2-out-of-3 property for rationality of motivic zeta function in
distinguished triangles in Voevodsky's category DM. As an application, we show
rationality of motivic zeta functions for all varieties whose motives are in
the thick triangulated monoidal subcategory generated by motives of
quasi-projective curves in DM. Joint with a result of P.O'Sullivan it also
gives an example of a variety whose motive is not finite-dimensional while the
motivic zeta function is rational.
