The effect of flow on the relaxation dynamics in entangled polymeric liquids can be investigated by superimposing small perturbations (in the form of step-strains, or of oscillating deformations) on top of steady flows. Recent experiments by Li and Wang [1] on parallel superposition flows of nearly monodisperse entangled polymer solutions revealing a flow-induced acceleration of the relaxation dynamics are here analyzed by using a simple differential constitutive equation based on the tube model [2] to examine the role of convective constraint release (CCR) in these situations. Contrary to the expectations of Wang and coworkers, we find that such a flow-induced acceleration is not a CCR effect. Rather, our results suggest that the acceleration is simply due to convection per se (not to be confused with CCR) and to nonlinear orientation effects [3]. [1] X. Li and S.Q. Wang, Macromolecules 43 (2010) 5904. [2] E. Somma, O. Valentino, G. Titomanlio and G. Ianniruberto, Journal of Rheology 51 (2007) 987. [3] H. J. Unidad and G. Ianniruberto, Rheologica Acta 53 (2014) 191.