The stacking interaction between pi systems is a well-recognized structural motif, but stacking between sigma systems was long considered of secondary importance. A recent paper points out that sigma stacking can reach the energy of chemical bonds and concludes that "sigma/sigma and pi/pi interactions are equally important" (Fokin, A. F.; Gerbig, D.; Schreiner, P. R. J. Am. Chem. Soc. 2011, 133, 20036). Our analysis shows that strong dispersion interaction requires rigid subsystems and good fits of their repulsive potential walls, conditions which are satisfied for both graphenes and larger graphanes (perhydrographenes). Comparison of the dimerization energies of decalin and perhydrocoronene with those of the naphthalene and coronene dimers at the coupled cluster (CC) CCSD(T) level confirms the substantial sigma-stacking energies in graphanes but shows lower binding energies than do the B97D calculations of Fokin et al. Graphane dimerization energies are substantially lower at the CC level than the corresponding pi-stacking energies: the value for perhydrocoronene is only 67% of the value for coronene, and the difference increases with system size. Our best estimate for the dimerization energy of naphthalene is 6.1 kcal/mol. Spin component scaled MP2 is unbalanced: it gives only 70% of the CCSD(T) binding energy in sigma dimers. The B3LYP-D3 method compares very well with CC for both sigma and pi dimers at the van der Waals minimum but underestimates the binding at larger distances. We used the largest possible atomic basis for these systems with 64-bit arithmetic, half-augmented-pVDZ, and the results were corrected for basis set incompleteness at the MP2 level.