A consistently unconstrained Brownian slip-link (CUBS) model with constant chain friction is used to predict the linear theological behavior of linear, entangled polymeric liquids. As in the previously proposed slip-link model without constraint release (J. Rheol. 2003, 47, 213), this model contains segment connectivity, contour-length fluctuations, and chain stretching in a self-consistent and natural way. Constraint release is considered in a mean-field way, but including fluctuations, both as a binary interaction between chains, and as a multichain interaction. Unlike previous mean-field works, constraint release is included on the level of chain dynamics instead of assuming that the relaxation modulation is a product of two moduli found by independent processes. These dynamics require no additional parameters. The model may also be used to make nonlinear flow predictions without any additional parameters. We find that inclusion of the additional physics of constraint release improves the linear viscoelastic predictions of the model, both for monodisperse polymers and bidisperse polymer blends. The difference between binary and multichain interaction predictions is not sufficiently large to distinguish comparisons with data within uncertainty.