  The essentially unique reduction of the Euler-Poinsot problem may be
performed in different sets of variables. Action-angle variables are usually
preferred because of their suitability for approaching perturbed rigid-body
motion. But they are just one among the variety of sets of canonical
coordinates that integrate the problem. We present an alternate set of
variables that, while allowing for similar performances than action-angles in
the study of perturbed problems, show an important advantage over them: Their
transformation from and to Andoyer variables is given in explicit form.
