Reducing the number of forwarding nodes is a primary objective in broadcast protocols for multi-hop wireless ad hoc networks, as excessive redundant transmissions lead to the broadcast storm problem. Existing approaches can be broadly categorized into proactive and reactive techniques, where proactive methods such as Dominant Pruning (DP) utilize forwarding lists based on multi-hop neighborhood information, while reactive approaches like Self-Pruning (SP) allow nodes to decide locally whether to rebroadcast. Improved Self-Pruning (ISB) enhances this process by incorporating extended neighborhood knowledge; however, it relies on degree-based pruning, which does not accurately capture the effective coverage contribution of neighboring nodes. In this paper, we propose an Enhanced Self-Pruning (ESP) algorithm that employs a coverage-aware pruning strategy using extended 3-hop neighborhood information. Unlike ISB, ESP determines forwarding decisions based on the comparison of effective uncovered neighbor sets rather than raw node degrees, and further refines pruning by incorporating lightweight grandparent information through packet piggybacking. Extensive simulation results demonstrate that ESP significantly reduces the number of forwarding nodes compared to ISB and DP, and also outperforms the Extended Dominant Pruning (ExDP) algorithm, while maintaining low control overhead. These results indicate that coverage-aware pruning combined with extended neighborhood knowledge provides a more scalable and efficient solution for broadcast dissemination in wireless ad hoc networks.