  We classify superpotentials for the Hamiltonian system corresponding to the
cohomogeneity one gradient Ricci soliton equations. Aside from recovering known
examples of superpotentials for steady solitons, we find a new superpotential
on a specific case of the B\'erard-Bergery-Calabi ansatz. The latter is used to
obtain an explicit formula for a steady complete soliton with an equidistant
family of hypersurfaces given by circle bundles over $S^2\times S^2$. There are
no superpotentials in the non-steady case in dimensions greater than 2, even if
polynomial coefficients are allowed. We also briefly discuss generalised first
integrals and the limitations of some known methods of finding them.
