A multi-stage fluid compression system includes a first centrifugal compressor stage having a first inlet and a first outlet and a second centrifugal compressor stage having a second inlet and a second outlet. The second inlet receives a flow of compressed fluid from the first outlet. A first variable-speed motor is coupled to the first centrifugal compressor stage and is operable to drive the first centrifugal compressor stage at a first speed. A second variable speed motor is coupled to the second centrifugal compressor stage and is operable to drive the second centrifugal compressor stage at a second speed. The first speed and the second speed are each independently variable.