The interplay between two important non-covalent interactions involving aromatic rings (namely anion-pi and hydrogen bonding) is investigated. Very interesting cooperativity effects are present in complexes where anion-pi and hydrogen bonding interactions coexist. These effects are found in systems where the distance between the anion and the hydrogen-bond donor/acceptor molecule is as long as approximately 11 A. These effects are studied theoretically using the energetic and geometric features of the complexes, which were computed using ab initio calculations. We use and discuss several criteria to analyze the mutual influence of the non-covalent interactions studied herein. In addition we use Bader's theory of atoms-in-molecules to characterize the interactions and to analyze the strengthening or weakening of the interactions depending upon the variation of the charge density at the critical points.