A reduced-dimensionality quantum model is proposed which incorporates the zero-point energy of the neglected modes in a systematic, natural way. In this model the reduced-dimensionality Hamiltonian is obtained by averaging the exact Hamiltonian over the dependence of the full-dimensional initial state of the neglected modes. The reduced Hamiltonian conserves all the terms of the full Hamiltonian, providing a more flexible description of the couplings between the modes considered explicitly in the model. The model is applied to simulate the vibrational predissociation dynamics of Cl-2-Ne-2, considering the three stretching modes of the complex. The results are compared to experimental data and to previous calculations using a reduced-dimensionality quantum model and a full-dimensional quantum-classical approach. The Cl-2-Ne-2 resonance lifetimes obtained agree only qualitatively with the experimental and previously calculated ones. By contrast, the present model predicts more correctly than previous calculations the behavior of the Cl-2 fragment vibrational distributions observed experimentally. The applicability of the model is discussed and further refinements are suggested.