Is a hydrogen bond symmetric, with the hydrogen centered between two donor atoms, or is it asymmetric, with the hydrogen closer to one but jumping to the other? The NMR method of isotopic perturbation has been used to distinguish these. Previous evidence from isotope shifts implies that a wide variety of dicarboxylate monanions are asymmetric, present as a rapidly equilibrating mixture of tautomers. However, calculations of hydrogen trajectories across an anharmonic potential-energy surface could reproduce the observed isotope shifts in a phthalate monoanion. Therefore, it was concluded that those isotope shifts are instead consistent with isotope-induced desymmetrization on a symmetric potential-energy surface. To distinguish between these two interpretations, the 18O-induced isotope effects on the 13C NMR chemical shifts of cyclohexene-1,2-dicarboxylate monoanion in chloroform-d and on the 19F NMR chemical shifts of difluoromaleate monoanion in D2O have been investigated. In both cases the isotope effects are larger at lower temperature and also with deuterium in the hydrogen bond. It is concluded that these behaviors are consistent with the perturbation of an equilibrium between asymmetric tautomers and inconsistent with isotope-induced desymmetrization on a symmetric potential-energy surface.