A method for controlling speed of an input shaft to a hydraulically actuated clutch that includes a hydraulic balance dam volume includes determining a limit speed of the input shaft that varies as a function of time during a predetermined period after the clutch starts rotation and that causes a servo piston for actuating the clutch to move toward an engaged position, rotating the input shaft during the period, limiting a speed of the input shaft during said period to a determined limit speed corresponding to a current time after beginning the period, and allowing the speed of the input shaft to increase to a speed greater than the determined limit speed after expiration of the period.