In a Letter by Lebegue et al. [Phys. Rev. Lett. 105, 196401 (2010)] describing benchmark ab initio adiabatic connection, fluctuation dissipation calculations under the random-phase approximation (ACFD-RPA) of graphite, it was demonstrated that the dispersion energy of uniaxially stretched graphite obeyed a van derWaals power law of the form U-vdW = -C3D-3 where D is the interlayer distance, in agreement with earlier theoretical models. However, the coefficient was found to be 0.125 eV angstrom(3)/atom in the calculations compared to 0.80 eV angstrom(3)/atom predicted by the theoretical models. In this work, we show that much of this discrepancy can be explained by the false assumption in the theoretical model that the Dirac cones extend infinitely rather than being confined to a finite-energy range, as in the numerical RPA work. We develop an improved model that takes into account this finite range via an imposed cutoff energy on transitions, and show that the dispersion energy is better represented by U-vdW approximate to -C3D-3[2/pi atan(D/D-c + phi)] where C-3 = 0.38 eV angstrom(3)/atom and D-c and phi depend on the finite-energy cutoff. This is of the same form as previously predicted for D ->infinity, but gives much better agreement with the ACFD-RPA results for appropriate values of the energy cutoff at intermediate layer spacings. The modified dispersion law will be important in the development of robust, general models of the interlayer graphitic potential.