In an earlier work [6], a localized broadcast authentication protocol was proposed to reduce verification delay in a large sensor network via using a few trusted nodes to divide sensor nodes into several sub areas and coordinate broadcast authentication in the sub areas. However, further study shows that the delay reduction is at the expense of increasing broadcast overhead due to updating localization information. Hence, the protocol in deployment can consume more energy of sensor nodes. To address the problem, we propose LD-TESLA to incorporate dominating nodes in broadcast authentication to eliminate redundant broadcast packets. The simulation illustrates that LD-TESLA can achieve significant reduction of broadcast overhead as well as verification delay. Compared with previous broadcast authentication protocols, LD-TESLA can save around 40% broadcast overhead.