Network wide broadcasting is an energy intensive function. In this paper we propose a new method that performs transmission power adaptations based on information available locally, to reduce the overall energy consumed per broadcast. In most of the prior work on energy efficient broadcasting it is assumed that the originator of the broadcast has global network information (both topology information as well as the geographical distance between nodes). This can be prohibitive in terms of the consumed overhead. In our protocol, each node attempts to tune its transmit power based on local information (of up to two hops from the transmitting node). We perform extensive simulations to evaluate our protocol. Our simulations take into account the possible loss of packets due to collision effects and the additional re-broadcasts that are necessary due to lower power transmissions.We show that our protocol achieves almost the same coverage as other non power-adaptive broadcast schemes but with a reduction of approximately 40 % in terms of the consumed power as compared to a scheme that does not adapt its power.