This paper introduces two kinds of decision tree ensembles for imbalanced classification problems, extensively utilizing properties of $\alpha$-divergence. First, a novel splitting criterion based on $\alpha$-divergence is shown to generalize several well-known splitting criteria such as those used in C4.5 and CART. When the $\alpha$-divergence splitting criterion is applied to imbalanced data, one can obtain decision trees that tend to be less correlated ($\alpha$-diversification) by varying the value of $\alpha$. This increased diversity in an ensemble of such trees improves AUROC values across a range of minority class priors. The second ensemble uses the same alpha trees as base classifiers, but uses a lift-aware stopping criterion during tree growth. The resultant ensemble produces a set of interpretable rules that provide higher lift values for a given coverage, a property that is much desirable in applications such as direct marketing. Experimental results across many class-imbalanced datasets, including BRFSS, and MIMIC datasets from the medical community and several sets from UCI and KEEL, are provided to highlight the effectiveness of the proposed ensembles over a wide range of data distributions and of class imbalance.