This paper deals with the problem of active damping of driveline oscillations in order to improve driveability and passenger comfort. Precisely, longitudinal vibrations occur during transient changes in driver demand, and they affect the driveability in a negative way. A robust and efficient controller is proposed, driving the engine in order to actively damp the driveline oscillations. The methodology considered is based on the prediction and compensation of the shaft torque at relevant frequencies. The main advantage and originality of the proposed approach consists in the simplicity of the design and the possibility to adjust the controller, directly on the vehicle, without redesign. This is made possible because the controller parameterization has a "physical" meaning. Three post-design tuning parameters are then available to manage the compromise between performance and robustness. The resulting controller is evaluated on a test car with a SI engine.