Nonmonotonic and even sign-changing dependences on the temperature and the doping level were predicted for the stationary Josephson tunnel current I-c between superconductors with d-wave order parameter symmetry and partial gapping by charge density waves (CDWs). The junction electrodes were considered in the framework of the two-dimensional electron spectrum appropriate to high-T-c cuprates. The non-trivial behavior can be observed for certain relative electrode orientations. Hence, I-c-measurements in wide ranges of doping and temperature may serve as an indicator of CDW existence. (C) 2015 Elsevier B.V. All rights reserved.