The "pom-pom" model of McLeish and Larson [J. Rheol. 42, 81-110 (1998)] provides a simple molecular theory for the nonlinear rheology of long chain branched polymer melts. A feature of this model is a maximum stretch for the branched molecules. Sharp transitions were predicted in the extensional viscosity at this maximum stretch. We introduce a simple treatment of the coupling between relaxed and unrelaxed polymer segments at branch points. The branch point is allowed to move in a quadratic localizing potential of unknown strength. Taking account of this effect smoothes the sharp transitions of the model and accounts for the extensional viscosity of "pom-pom" model polymers at their maximum stretch. The result is an improved multimode pom-pom fit for low-density polyethylene rheology. By fitting the nonlinear extensional viscosity, quantitative predictions are made for the nonlinear steady shear viscosity and transient first normal stress difference in shear. (C) 2000 The Society of Rheology. [S0148-6055(00)00701-X].