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The capability of accurately estimating an upper bound of the maximum current drawn by a digital macroblock from the ground or power supply line constitutes a major asset of automatic power-gating flows. In fact, the maximum current information is essential to properly size the sleep transistor in such a way that speed degradation and signal integrity violations are avoided. Loose upper bounds can be determined with a reasonable computational cost, but they lead to oversized sleep transistors. On the other hand, exact computation of the maximum drawn current is an NP-hard problem, even when conservative simplifying assumptions are made on gate-level current profiles. In this paper, we present a scalable algorithm for tightening upper bound computation, with a controlled and tunable computational cost. The algorithm exploits state-of-the-art commercial timing analysis engines, and it is tightly integrated into an industrial power-gating flow for leakage power reduction. The results we have obtained on large circuits demonstrate the scalability and effectiveness of our estimation approach.