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A fact that has generally been unnoticed is that sleep transistors for leakage reduction can significantly damp the resonant supply noise due to their series resistance. This paper describes an optimal sleep transistor sizing method considering the dominant resonant supply noise. We show that a smaller sleep transistor can offer a smaller worst case supply noise due to the increased damping. We also propose an adaptive sleep transistor technique which automatically dampens the resonant noise only when it is detected. Simulations in 32nm CMOS show that the resonant noise is reduced by 32% using the proposed technique.