  We present a method for constructing classically perfect anisotropic actions
for SU(3) gauge theory based on an isotropic Fixed Point Action. The action is
parametrised using smeared (``fat'') links. The construction is done explicitly
for anisotropy $\xi=a_s/a_t=2$ and 4. The corresponding renormalised
anisotropies are determined using the torelon dispersion relation. The
renormalisation of the anisotropy is small and the parametrisation describes
the true action well. Quantities such as the static quark-antiquark potential,
the critical temperature of the deconfining phase transition and the low-lying
glueball spectrum are measured on lattices with anisotropy $\xi=2$. The mass of
the scalar $0^{++}$ glueball is determined to be 1580(60) MeV, while the tensor
$2^{++}$ glueball is at 2430(60) MeV.
