  We give an algorithm to compute the stable lengths of pseudo-Anosovs on the
curve graph, answering a question of Bowditch. We also give a procedure to
compute all invariant tight geodesic axes of pseudo-Anosovs.
  Along the way we show that there are constants $1<a_1<a_2$ such that the
minimal upper bound on `slices' of tight geodesics is bounded below and above
by $a_1^{\xi(S)}$ and $a_2^{\xi(S)}$, where $\xi(S)$ is the complexity of the
surface. As a consequence, we give the first computable bounds on the
asymptotic dimension of curve graphs and mapping class groups.
  Our techniques involve a generalization of Masur--Minsky's tight geodesics
and a new class of paths on which their tightening procedure works.
