Orbits that respect at least three isolating integrals of motion have very special structures in phase space. The main characteristics of this structure are reviewed, and the concrete examples that are provided by orbits in Stäckel potentials, are discussed. Many orbits in general potentials admit three approximate isolating integrals and closely resemble orbits in Stäckel potentials. If the potential is that of an elliptical galaxy with negligible figure rotation, the overall orbital stucture of the potential differs from that of a Stäckel potential only by the presence of a few unimportant families of resonant orbits. However, this elegant picture is shattered by the introduction of non-negligible figure rotation: though substantial regions of phase space may still be occupied by orbits that individually resemble orbits in Stäckel potentials, the overall orbital structure is radically changed by figure rotation, and in a rotating potential significant portions of phase space are given over to chaotic orbits, quite unlike orbits in Stäckel potentials.