  We summarize our recent work on the construction and properties of fixed
point (FP) actions for lattice $SU(3)$ pure gauge theory. These actions have
scale invariant instanton solutions and their spectrum is exact through
1--loop, i.e. in their physical predictions there are no $a^n$ nor $g^2 a^n$
cut--off effects for any $n$. We present a few-parameter approximation to a
classical FP action which is valid for short correlation lengths. We perform a
scaling test of the action by computing the quantity $G = L \sqrt{\sigma(L)}$,
where the string tension $\sigma(L)$ is measured from the torelon mass $\mu = L
\sigma(L)$, on lattices of fixed physical volume and varying lattice spacing
$a$. While the Wilson action shows scaling violations of about ten per cent,
the approximate fixed point action scales within the statistical errors for $
1/2 \ge aT_c$.
