Isotope effect calculations (H/D and O-16/O-18) were carried out for a series of vibrational models containing a double-minimum potential for a hydrogen bond. The calculations showed the maximum hydrogen isotope effects for models in which the zero-point vibrational levels (for H) for the motion governed by the double-minimum potential were very near the energy of the barrier for the potential. The hydrogen isotope effects also showed a strong dependence on the energy difference between the wells of the double-minimum potential. Isotopic entropies were calculated for the H/D isotope effects, and were found to be dependent on the height of the barrier in the potential. Oxygen isotope effects were all inverse for reasons having little to do with the presence of double-minimum potentials in the models. The results have implications for studies of low-barrier hydrogen bonds.