We introduce a generalized representation for a boosted classifier with multiple exit nodes, and propose a method to training which combines the idea of propagating scores across boosted classifiers [14,17] and the use of asymmetric goals [13]. A means for determining the ideal constant asymmetric goal is provided, which is theoretically justified under a conservative bound on the ROC operating point target and empirically near-optimal under the exact bound. Moreover, our method automatically minimizes the number of weak classifiers, avoiding the need to retrain a boosted classifier multiple times for empirical best performance as in conventional methods. Experimental results shows significant reduction in training time and number of weak classifiers, as well as better accuracy, compared to conventional cascades and multi-exit boosted classifiers.