A promising new constitutive equation for polymer melts is herein presented, one that contains both the Lodge or upper‐convected Maxwell model and a good approximation to the Doi‐Edwards model as special cases. The upper‐convected Maxwell model is one of the most basic while the Doi‐Edwards model is the one perhaps most surely founded on molecular principles. The differential model presented here is based on molecular reasoning that should be particularly well suited to commercial, highly branched melts such as low‐density polyethylene. The idea behind the model is that long side branches can limit the extent to which a polymer strand is able to contract back within the confining tubelike region postulated by Doi and Edwards.