A graph-based iterative method is provided for selecting component modifications in an integrated circuit design that reduce the power consumption to a minimum while still meeting timing constraints. Channel-connected components are represented as nodes in a timing graph and edges in the timing graph represent directed paths. From the timing graph, a move graph is constructed containing a plurality of move nodes. Each move node represents a change to one of the components in one of the timing graph nodes. A given timing graph node can result in a plurality of move nodes. Move nodes can be merged into group nodes, and both the move nodes and group nodes are assigned a weight based on the change in power and timing effects of the associated components changes. These weights are used to select move nodes or group nodes. In general, a set of move or group nodes is selected representing the maximum cumulative weight and the components changes associated with the nodes in the set are performed on the integrated circuit design. Moves that cause timing violations are reversed. The node weights are updated following components changes and the selection of node sets is repeated iteratively until the power consumption converges to a minimum.