A three-phase decanting centrifuge is provided. Solids are removed from a slurry in the centrifuge in the conventional manner, as described above. The liquid separated from the slurry moves into a fluids reservoir. Centrifugal action classifies the fluids, with lighter fluids (typically oil) radially closer to the axis of rotation of the machine, while the heavier fluids are radially farther from the axis, i.e. at the bottom of the reservoir. Lighter fluids flow out a plurality of overflow tubes. Heavier fluids flow through a plurality of ports into a heavy fluids reservoir to be skimmed out by a pair of radially actuatable skimmer tubes. The skimmer tubes are preferably automatically operated based on the light transmissivity of the lighter and heavier fluids discharged from the machine.