The machine may have a power system that includes a prime mover, a multiple-ratio transmission, a propulsion device, and power-system controls. The method may include propelling the machine by transmitting power from the prime mover to the propulsion device through the multiple-ratio transmission, while controlling operation of the prime mover and the multiple-ratio transmission with the power-system controls. This may include determining with the power-system controls at least one energy-efficiency estimate based at least on energy-efficiency characteristics of the prime mover and energy-efficiency characteristics of the multiple-ratio transmission. Controlling the prime mover and the multiple-ratio transmission may further include controlling a prime-mover operating speed of the prime mover and a transmission drive ratio of the multiple-ratio transmission based at least in-part on the at least one energy-efficiency estimate.