Low-temperature specific heat of CDW compounds ZrTe3 and NbTe4, measured between 1.5 and 10 K, exhibited an anomaly which deviates from the regular phonon term; an excess specific-heat contribution appeared around T = 6 K. The excess contribution was well presented in terms of the phason contribution of CDW. The pinning frequency estimated from the analysis was quite high in comparison to the value of common CDW conductors, which is not inconsistent with the linear relation between current and voltage. (C) 2003 Elsevier Science B.V. All rights reserved.