In this paper, we propose Max-diverse.α, which has a mechanism to control the degrees of randomness in decision tree ensembles. This control gives an ensemble the means to balance the two conflicting functions of a random random ensemble, i.e., the abilities to model non-axis-parallel boundary and eliminate irrelevant features. We find that this control is more sensitive to the one provided by Random Forests. Using progressive training errors, we are able to estimate an appropriate randomness for any given data prior to any predictive tasks. Experiment results show that Max-diverse.α is significantly better than Random Forests and Max-diverse Ensemble, and it is comparable to the state-of-the-art C5 boosting.