Unlike in a wired network, a packet transmitted by a node in an ad hoc wireless network can reach all neighbors. Therefore, the total number of transmissions (forward nodes) is generally used as the cost criterion for broadcasting. The problem of finding the minimum number of forward nodes is NP-complete. Among various approximation approaches, dominant pruning (Lim and Kim 2001) utilizes 2-hop neighborhood information to reduce redundant transmissions. In this paper, we analyze some deficiencies of the dominant pruning algorithm and propose two better approximation algorithms: total dominant pruning and partial dominant pruning. Both algorithms utilize 2-hop neighborhood information more effectively to reduce redundant transmissions. Simulation results of applying these two algorithms show performance improvements compared with the original dominant pruning. In addition, two termination criteria are discussed and compared through simulation under both the static and dynamic environments.