We introduce a new algorithm to achieve a distributed leader election in a broadcast channel that is more efficient than the classic Part-and-Try algorithm. The algorithm has the adavantage of having a reduced overhead $\log\log N$ rather than $\log N$. More importantly the algorithm has the a greatly reduced energy consumption since it requires $O(N^{1/k})$ burst transmissions instead of $O(N/k)$, per election, $k$ being a parameter depending on the physical properties of the medium of communication. The algorithm has interesting potential applications in wireless cognitive networking.