Broadcasting is an important communication mechanism in ad hoc wireless networks. The simplest way to do broadcasting is pure flooding, in which each node retransmits a packet after receiving it, thus generates many redundant retransmissions. The rule based on dominating sets can reduce the number of retransmissions. A dominating set is a set of nodes such that any node in the network is a neighbor of some element in the set. However, computing a minimum size connected dominating set is NP hard. Several existing algorithms use the idea of multipoint relays to reduce the size of the connected dominating set. The authors of this paper observed that these algorithms can be further improved. Thus, three improvements are introduced here. It is proved that these improvements can compute a connected dominating set of the network, and simulation results show that they can further reduce the size of the dominating set. Also, extensions to power-aware broadcasting algorithms are discussed.