Byzantine Generals algorithms enable processes to reliably broadcast messages in a system of $n$ processes where up to $t$ of the processes may be faulty. The algorithms are conducted in synchronous rounds of message exchange. For a system where $n=(3+\delta )t$ we prove the existence of a randomized algorithm whose expected number of rounds is $O(lgn)$. This is an improvement on the lower bound of $t+1$ rounds required for deterministic algorithms and on the previous result of $t/lgn$ expected number of rounds for randomized algorithms.