Abstract: A hydrokinetic torque converter including a secondary piston for purposes of enhancing operation of the lock-up feature, and the method of operating such a converter. The secondary piston moves axially behind the turbine-piston to urge respective lock-up clutch friction surfaces into phased engagement. In an initial phase of engagement, friction surfaces between the secondary piston and turbine-piston engage to begin the reduction of relative rotary motion between the converter impeller and turbine-piston. This initial phase of slowing relative movement between the impeller and turbine-piston reduces pressure within the torus and the associated fluid forces separating the friction surfaces of the lock-up clutch. The secondary piston also slows and eliminates fluid flow from within the torus past the lock-up clutch and further reduces engagement resistance of the lock-up clutch owing to the lessening fluid pressure and flow.