Starting from a multiresonance spectroscopic Hamiltonian fit by Baggott to experimental levels of H2O, an approximate Hamiltonian is devised using a prediagonalized "dressed" zero-order basis, within which a residual, effective single-resonance coupling operator acts. The dressed basis incorporates many of the effects of nonintegrability, while the effective resonance furnishes much of the simplicity of integrable systems. Numerical tests are performed for two distinct dressed bases, in which different resonance operators are chosen as the residual effective coupling. Excellent agreement with the energies and eigenvectors of the exact system is obtained for each of the two dressed bases. (C) 2003 American Institute of Physics.