In melts of asymmetric three-arm star polymers in which a short arm is attached to two long, equal-length arms, the existing "tube" theory fails to predict how rapidly the motion of the branchpoint becomes quenched when the length of the third, short, arm grows from zero length, for which the two other arms form a reptating linear chain, to a length equal to the other two arms, for which reptation is quenched. We use a simulation method that represents entanglements between two chains as "sliplinks" that allow local relaxation of both chains when an end of either chain passes through the slip-link. We include an extreme form of branch-point motion in this algorithm and find that it can explain the anomalously rapid quenching of the branch-point if we assume that the time scale of the branch-point motion is set by the time required for the short arm to escape all entanglements, including those newly created while others are destroyed. The algorithm successfully predicts the linear viscoelasticity of H-polymers, where the acceleration induced by the polydispersity offsets the sluggishness introduced by adopting a drastically slow time scale for diffusion of the branch-point. Although the theory becomes unrealistic for long arms, it raises important questions about existing theories of branch-point motion and provides some clues to their resolution.