In this paper we present a new approximation algorithm for the Minimum Energy Broadcast Routing (MEBR) problem in ad hoc wireless networks that has exponentially better approximation factor than the well-known Minimum Spanning Tree (MST) heuristic. Namely, for any instance where a minimum spanning tree of the set of stations is guaranteed to cost at most ½ times the cost of an optimal solution for MEBR, we prove that our algorithm achieves an approximation ra- tio bounded by 2 ln ½ ¡ 2 ln 2 + 2. This result is particularly relevant for its consequences on Euclidean instances where we signi¯cantly improve previous results.