Rotational energy surfaces [W. G. Harter and C. W. Patterson, J. Chem. Phys. 80, 4241 (1984)] for a molecule with internal rotation are constructed. The study is limited to torsional states at or below the top of the barrier to internal rotation, where the extra (torsional) degree of freedom can be eliminated by expanding eigenvalues of the torsion-K-rotation Hamiltonian as a Fourier series in the rotational degree of freedom. For acetaldehyde, considered as an example, this corresponds to considering upsilon(t)=0, 1, and 2 (below the barrier) and upsilon(t)=3 (just above the barrier). The rotational energy surfaces are characterized by locating their stationary points (maxima, minima, and saddles) and separatrices. Rather complicated catastrophe histories describing the creation and annihilation of pairs of stationary points as a function of J are found at moderate J for given torsional quantum number (upsilon(t)) and symmetry species (A,E). Trajectories on the rotational energy surface which quantize the action are examined, and changes from rotational to vibrational trajectories caused by changes in the separatrix structure are found as a function of J for upsilon(t)=2. The concept of a "best" quantization axis for the molecule-fixed component of the total angular momentum is examined from a classical point of view, and it is shown that labeling ambiguities encountered in the literature for torsion-rotation energy levels, calculated numerically in the rho-axis system, can be eliminated by reprojecting basis-set K values onto an axis passing through an appropriate stationary point on the rotational energy surface.