AdaBoost and other ensemble methods have successfully been applied to a number of classification tasks' seemingly defying problems of overfitting. AdaBoost performs gradient descent in an error function with respect to the margin' asymptotically concentrating on the patterns which are hardest to learn. For very noisy problems' however' this can be disadvantageous. Indeed' theoretical analysis has shown that the margin distribution' as opposed to just the minimal margin' plays a crucial role in understanding this phenomenon. Loosely speaking' some outliers should be tolerated if this has the benefit of substantially the margin on the remaining points. We propose a new boosting algorithm which allows for the possibility of a pre-specified fraction of points to lie in the margin area or even on the wrong side of the decision boundary.