Secondary deuterium isotope effects (IEs) on acidities have been accurately measured by an NMR titration method applicable to a mixture of isotopologues. Deuteration definitely decreases the acidity of carboxylic acids and phenols, by up to 0.031 in the Delta pK per D. For aliphatic acids, the IEs decrease as the site of deuteration becomes more distant from the OH, as expected, but a surprising result is that IEs in both phenol and benzoic acid do not decrease as the site of deuteration moves from ortho to meta to para. The experimental data are supported by ab initio computations, which, however, substantially overestimate the IEs. The discrepancy does not seem to be due to solvation. The IEs originate in isotope-sensitive vibrations whose frequencies and zero-point energies are lowered upon deprotonation. In the simplest case, formate, the key vibration can be recognized as the C-H stretch, which is weakened by delocalization of the oxygen lone pairs. For the aromatic acids, delocalization cannot account for the near constancy of IEs from ortho, meta, and para deuteriums, but the observed IEs are consistent with calculated vibrational frequencies and electron densities. Moreover, the ability of the frequency analysis to account for the IEs is evidence against an inductive origin.