  We give an algorithm for the economical calculation of angles and actions for
stars in axisymmetric potentials. We test the algorithm by integrating orbits
in a realistic model of the Galactic potential, and find that, even for orbits
characteristic of thick-disc stars, the errors in the actions are typically
smaller than 2 percent. We describe a scheme for obtaining actions by
interpolation on tabulated values that significantly accelerates the process of
calculating observables quantities, such as density and velocity moments, from
a distribution function.
