In many electrolyte solutions, ions of opposite signs can be paired due to electrostatic or more specific interactions. The pairing may occur in competition with the individual solvation of the ions. Some of the solvent molecules, initially present around each of the ions, may be excluded between pairing ions. The resulting complexes can be seen as dumbbells with a strong overlap between the spheres representing each of the hydrated ions involved in the association. The thermodynamic description of electrolyte solutions containing such pairing ions is described in this paper with a variational generalisation of the binding mean spherical approximation