The double-reptation ansatz for stress relaxation in broadly polydisperse melts of linear chains relates the molecular weight distribution phi(n) and the dynamic viscosity eta(omega), and has been used to infer phi(n) from rheological data. I show that the microscopic theory of constraint release implies the double-reptation model is valid for practical distributions phi(n). I also provide a heuristic theoretical argument for the Cox-Merz empirical rule that the shapes of the functions eta*omega and eta(gamma over dot) are similar, which allows the shear-thinning curve to be predicted.