Pure 3d gravity in AdS has only boundary degrees of freedom. I will show that these interact nontrivially if spacetime is restricted to a finite size. Their dynamics can be obtained equivalently by TTbar deforming the infinite volume theory. We can canonically quantize the gravitational side and, after a field redefinition, find a simple description of this system as a Nambu-Goto action with a gauged zero-mode and a specific and a non-canonical stress tensor. The correlation functions, calculated perturbatively in the deformation parameter, provide insight into what is completely determined and what may remain unfixed in TTbar deformed theories.