The MP2C dispersion correction of Pitonak and Hesselmann [J. Chem. Theory Comput. 6, 168 (2010)] substantially improves the performance of second-order Møller-Plesset perturbation theory for non-covalent interactions, albeit with non-trivial computational cost. Here, the MP2C correction is computed in a monomer-centered basis instead of a dimer-centered one. When applied to a single dimer MP2 calculation, this change accelerates the MP2C dispersion correction several-fold while introducing only trivial new errors. More significantly, in the context of fragment-based molecular crystal studies, combination of the new monomer basis algorithm and the periodic symmetry of the crystal reduces the cost of computing the dispersion correction by two orders of magnitude. This speed-up reduces the MP2C dispersion correction calculation from a significant computational expense to a negligible one in crystals like aspirin or oxalyl dihydrazide, without compromising accuracy.