  For a general three dimensional theory of (super-)gravity coupled to
arbitrary matter fields with arbitrary set of higher derivative terms in the
effective action, we give an algorithm for consistently truncating the theory
to a theory of pure (super-)gravity with the gravitational sector containing
only Einstein-Hilbert, cosmological constant and Chern-Simons terms. We also
outline the procedure for finding the parameters of the truncated theory. As an
example we consider dimensional reduction on S^2 of the 5-dimensional minimal
supergravity with curvature squared terms and obtain the truncated theory
without any curvature squared terms. This truncated theory reproduces correctly
the exact central charge of the boundary CFT.
