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We address the problem of minimizing dynamic power consumption under performance constraints by scaling down the supply voltage of computational elements off critical paths. We assume that the number of possible supply voltages and their values are known for each computational element. We focus on solving this problem on cyclic and acyclic graphs corresponding to synchronous designs. We consider multiphase clocked sequential circuits derived using software pipelining techniques. In this paper, we present exact and heuristic methods to solve the problem. The proposed methods take the form of mathematical programming formulations and their associated solution algorithms. The exact methods are based on a mixed integer linear programming formulation of the problem. The heuristic methods are based on linear programming formulations derived from the exact problem formulation. Solution methods are analyzed experimentally in terms of their run time and effectiveness in finding designs with lower dynamic power using circuits from the ISCAS89 benchmark suite. Power reduction factors as high as 69.75% were obtained compared to designs using the highest supply voltages. One of the heuristic methods leads to solutions that are near optimal, typically within 5% from the optimal solution. Low dynamic-power designs with no or a small number of level converters, are also obtained.