A powertrain system including an internal combustion engine rotatably coupled to a variator of a continuously variable transmission (CVT) is described. A method for controlling the CVT includes determining a desired variator speed ratio in response to a command to increase output power from the powertrain system and executing a step-down shift in the CVT based upon the desired variator speed ratio, the step-down shift. The step-down shift includes determining a preferred CVT input acceleration profile based upon the desired variator speed ratio, a present variator speed ratio, and a preferred shift time and synchronizing the preferred CVT input acceleration profile with engine torque. A change rate for the variator speed ratio is based upon the preferred CVT input acceleration profile, and the CVT is controlled in response to the change rate for the variator speed ratio and the desired variator speed ratio.