The desymmetrizing effect of isotopic substitution on the geometry of otherwise symmetrical structures can be surprisingly large when there is anharmonic coupling between a desymmetrizing mode and modes whose zero-point energies are strongly isotope-dependent. This phenomenon is found to account for experimental observations that had been previously interpreted as implying asymmetry in bromonium ions and in hydrogen phthalate ions in aprotic solvents. The unlabeled structures are concluded to have the higher symmetry found in computed structures. Great care must be taken in applying isotopic perturbation as a test of asymmetry.