Stacking interactions between substituted buckybowls (corannulene and sumanene) with fullerenes (C-60 and C-70) were studied at the B97-D2/TZVP level of theory. Corannulene and sumanene monomers were substituted with five and six Br, Cl, CH3, C2H, or CN units, respectively. A comprehensive study was conducted, analyzing the interaction of corannulenes and sumanenes with several faces of both fullerenes. According to our results, in all cases substitution gave rise to larger interaction energies if compared with those of unsubstituted buckybowls. The increase of dispersion seems to be the main source of the enhanced binding, so an excellent correlation between the increase of interaction energy and the increase of dispersion contribution takes place. One of the noteworthy phenomena that appears is the so-called CH center dot center dot center dot pi interaction, which is responsible for the strong interaction of sumanene complexes (if compared with that of corannulene complexes). This interaction also causes the substitution with CH3 groups (in which one of the H atoms points directly to the pi cloud of fullerene) to be the most favorable case. This fact can be easily visualized by noncovalent interaction plots.