Scalability and power-efficiency are two of the most important design challenges in wireless ad hoc networks. In this paper, we present a scalable, power-efficient broadcast algorithm for wireless ad hoc networks. We first investigate the trade-off between (i) reaching more nodes in a single hop using higher transmission power and (ii) reaching fewer nodes using lower transmission power and relaying messages through multiple hops. Our analysis indicates that multi-hop broadcast is more power-efficient if α ≥ 2.2, where α is the path loss exponent in the power consumption model P(r,α) = c0α rα+c1. Based on the analysis, we then propose Broadcast over Local Spanning Subgraph (BLSS). In BLSS, an underlying topology is first constructed by a localized topology control algorithm, Fault-Tolerant Local Spanning Subgraph (FLSS). FLSS can preserve k-connectivity of the network, where the value of k determines the degree of fault tolerance. Broadcast messages are then simply relayed through the derived topology in a constrained flooding fashion. BLSS is fully localized, scalable, power-efficient, and fault-tolerant. Simulation results show that the performance of BLSS is comparable to that of centralized algorithms.