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In ad hoc wireless networks, due to node mobility, broadcasting is expected to be more frequent to update global route/network information. A straightforward broadcasting by flooding is usually very costly and will result in substantial redundancy and large energy consumption. Power consumption is an important issue since most mobile hosts operate on battery. Broadcasting based on a connected dominating set (CDS) is a promising approach, where only nodes in the CDS need to relay the broadcast message. A set is dominating if all the nodes in the system are either in the set or neighbors of nodes in the set. In general, nodes in the CDS consume more energy to handle various bypass traffic than nodes outside the set. To prolong the life span of each node and, hence, the network, nodes should be alternated when possible to form a CDS. In this paper, we further extend the power-aware broadcasting by dynamically reducing the transmission range of each node during the broadcast process without sacrificing the broadcast coverage. The effectiveness of the proposed methods in prolonging the life span of the network is confirmed through simulation.