We compare the Rubinstein - Duke model for reptation to a model where the boundary dynamics are modified by calculating the viscosity of polymer melts. The question is investigated whether the viscosity is determined by details of the dynamics of the polymer ends or by the stretching of the polymer. Toward this end, the dependence of the viscosity on the particle density of the lattice gas models which can be identified by the stretching is determined. We show that the influence of the stretching of the polymer on the absolute value of the viscosity in the scaling limit of very long chains is much bigger than the influence of the boundary dynamics, whereas the corrections of the scaling of the viscosity depends significantly on the details of the boundary dynamics. (C) 2003 American Institute of Physics.