A new implementation of constraint dynamics for the discrete slip-link model (DSM), which is statistically consistent with sliding dynamics of the chain, is proposed. The DSM agrees with linear viscoelastic (LVE) data for linear monodisperse entangled polymer melts at least as well as state-of-the-art tube models. The agreement with data can be obtained by fitting only two parameters, beta and tau(K) that are independent of the molecular weight of the polymer. However, because the theory exists on a more-detailed level of description, it contains fewer assumptions than do existing tube models and assumptions of the latter may be examined. Several fundamental differences between DSM and tube models are revealed. For example, Rouse motion is an inappropriate realization of constraint dynamics in the slip-link picture. Moreover, the chain relaxation by sliding dynamics for the DSM is significantly different from the fraction of survived entanglements multiplied by the plateau modulus, whereas the tube model assumes that these are equivalent at long times. These two differences effectively cancel one another. Moreover, they could result in different bidisperse LVE predictions. On the other band, several other assumptions made in tube theories are confirmed by the DSM results. Finally, model comparisons with experimental data exposed some limitations in the experiments.