We present a systematic computational analysis of the conformations and stacking interactions of a set of 18 saddle-shaped, contorted polycyclic aromatic compounds at the B97-D3M(BJ)/TZV(2d,2p)//B97-D/TZV(2d,2p) level of theory. These doubly-concave systems offer a means of tuning the strength of stacking interactions through variations in molecular curvature, and understanding the intermolecular non-covalent interactions exhibited by these systems will aid the design of contorted polycyclic systems with precisely defined packing in the solid state. Computations reveal wide variations in both the nature of the low-lying conformations and the stacking affinities of these systems. In particular, the introduction of both thiophene rings around the periphery of these systems and the incorporation of B and N atoms into the coronene core can greatly enhance their tendency to form strongly stacked dimers. Overall, these data provide a reminder that curvature does not always lead to stronger stacking interactions.