In recent work Long and Servedio \cite{LS05short} presented a martingale boosting'' algorithm that works by constructing a branching program over weak classifiers and has a simple analysis based on elementary properties of random walks. \cite{LS05short} showed that this martingale booster can tolerate random classification noise when it is run with a noise-tolerant weak learner; however, a drawback of the algorithm is that it is not \emph{adaptive}, i.e. it cannot effectively take advantage of variation in the quality of the weak classifiers it receives.