  We use a set of Stackel potentials to obtain a local approximation for an
effective third integral in axisymmetric systems. We present a study on the
feasibility and effectiveness of this approach. We have applied it to three
trial potentials of various flattenings, corresponding to nearly ellipsoidal,
disky and boxy density isophotes. In all three cases, a good fit to the
potential requires only a small set of Stackel potentials, and the associated
Stackel third integral provides a very satisfactory, yet analytically simple,
approximation to the trial potentials effective third integral.
