The present work reports a discrete stress-dependent, complex compliance spectra method that may be used to predict the mechanical response of nonlinear viscoelastic polymers during creep and recovery processes. The method is based on the observation that the real and imaginary parts of a discrete complex compliance frequency spectra obtained from creep and recovery measurements are smooth, easily fit functions of stress. The new method is applied to a set of microcellular polycarbonate materials with differing relative density. The nonlinear viscoelastic characteristics of a microcellular polycarbonate material system are very sensitive to relative density and therefore, this material system is a particularly difficult modeling challenge. However, the present model was able to exhibit excellent quantitative agreement with the basis creep and recovery measurements at all experimental stress levels for each of the experimental relative density material types.