A consistently unconstrained Brownian slip-link model (CUBS) with constant chain friction is used to predict the nonlinear theological behavior of linear, entangled, polymeric liquids. The model naturally incorporates primitive-path-length fluctuations, segment connectivity, monomer density fluctuations, entanglement fluctuations, and constraint release without making any closure approximations. Constraint release is imposed on the level of the dynamics of the chain, and the relaxation modulus follows from these rigorously. The model is a mean-field, single-chain slip-link model, or temporary network model, with a single phenomenological time constant, tau(e), fit by linear viscoelasticity. The nonlinear flow predictions are made without adjusting any additional parameters. We find that the addition of constant chain friction noticeably improves the model predictions in all the flows considered. In contradiction with tube models, the results suggest that the additional physics of constraint release and convective constraint release are not very important in predicting the nonlinear shear properties, except at low shear rates (close to the LVE regime). (c) 2007 The Society of Rheology.