A three-dimensional model of the vibrational dynamics of HOONO is investigated. This model focuses oil the couplings between the OH stretch vibration and the two torsions. The model is based oil electronic energies, calculated at the CCSD(T)/cc-pVTZ level of theory and basis and dipole moment functions calculated at the CCSD/aug-cc-pVDZ level. The resulting points were fit to explicit functional forms, and the energies, wave functions, and intensities were evaluated using an approach in which the OH stretching motion was adiabatically separated from the torsional modes. It is found that the HOON torsion is strongly coupled to both the OONO torsion and OH stretch. Despite this, many of the conclusions that were drawn from earlier two-dimensional treatments, which did not include the OONO torsion, hold tip on a semiquantitative level. In addition, we use this model to investigate the assignment of recently reported matrix isolated spectra of HOONO and DOONO. Finally, by comparing the results of this three-dimensional calculation to two-dimensional calculations and to the results of second-order perturbation theory, we investigate the question of how one determines the size of the reduced-dimensional system that is needed to describe the vibrational spectrum Of molecules, like HOONO, that contain several large amplitude motions.