We investigate the dissipative dynamics of a Morse oscillator coupled nonlinearly to a heat bath. To this end, we compare several reduced equations of motion with the dynamics of a full-dimensional wave packet with up to 61 spatial degrees of freedom. The discretized bath is converged for the relevant times considered in this paper. The propagations are done with a general purpose implementation of the multiconfiguration time-dependent Hartree method. (C) 2003 American Institute of Physics.