Goodman, Greenberg, Madras and March gave a lower bound of n^-W(logn)]]> for the maximum arrival rate for which the n-user binary exponential backoff protocol is stable. Thus, they showed that the protocol is stable as long as the arrival rate is at most n^-W(logn)]]>. We improve the lower bound, showing that the protocol is stable for arrival rates up to O(n^-.9).