  On anisotropic lattices, where generally the lattice is rather coarse in
spatial directions, a parametrized classically perfect action could help
reducing lattice artifacts considerably. We investigate the possibility of
constructing such actions for SU(3) gauge theory. We present two different
methods to do so, either repeating the procedure used to create our newly
parametrized isotropic FP action, or performing one single step starting with
the isotropic result. The anisotropic action is parametrized using an ansatz
including anisotropically APE-like smeared (``fat'') links. The parametrized
classically perfect action with anisotropy $\xi=a_s/a_t=2$ is constructed and
the renormalized anisotropy is measured using the torelon dispersion relation.
It turns out that the renormalization is small.
