Full configuration interaction calculations for two electrons moving in the field of an electric dipole have been carried out in order to determine whether bound states with respect to detachment of one electron exist. Model dipoles are constructed by the placement of point charges q=1, 2, 3 a.u. at varying distances. It was found that for a dipole constructed of point charges q=3 separated by a distance of 0.8788 a.u., the energy of binding one and two electrons is equivalent. In all cases, there exist charge separation lengths for which the binding of two electrons gives a binding energy only slightly less than that of binding one electron. Escape channels were not calculated, but may provide barriers allowing the existence of dipole-bound dianions with lifetimes long enough to allow detection.