Dispersion corrections, namely the D3 and VV10 methodologies, have been added to the TCA GGA-like family of functionals. Without corrections, these functionals give very good results for iono-covalent systems, but they are inferior to other GGAs (e.g., PBE) for weakly interacting complexes. Applying dispersion corrections, this failure is completely overcome. In particular, RevTCA, which is the best functional for iono-covalent systems, becomes the best for weakly interacting complexes too, with mean absolute errors very often smaller than one tenth of \AA for the geometries and 1 kcal/mol for the dissociation energies.