A method regulates a machine having a continuously variable transmission (CVT) and service brakes in a manner to reduce power transmission through the applied brakes. The method utilizes an unaltered torque-to-speed curve that relates the torque output to the speed output of the CVT. An under-run curve may be applied to the torque-to-speed curve and that corresponds to a target speed. The method may receive an operator input signal indicative of a braking event. In response, the method may shift the torque-to-speed curve to limit the output torque available. The method may also adjust the under-run curve in a manner that maintains correspondence with the target speed.