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Micro-channel cooling shows great potential in removing high density heat in 3D circuits. The current micro-channel heat sink designs spread the entire surface to be cooled with micro-channels. This approach, though might provide sufficient cooling, requires quite high pumping power. In this paper, we investigate the non-uniform allocation of micro-channels to provide sufficient cooling with less pumping power. Specifically, we decide the count, location and pumping pressure drop/flow rate of micro-channels such that acceptable cooling is achieved at minimum pumping power. Thermal wake effect and runtime pressure drop/flow rate control are also considered. The experiments showed that, compared with the conventional design which spreads micro-channels all over the chip, our non-uniform micro-channel design achieves 55-60% pumping power saving.