Quality Diversity (QD) algorithms are a class of population-based evolutionary algorithms designed to generate sets of solutions that are both fit and diverse. In this paper, we describe a strategy for applying QD concepts to the generation of decision tree ensembles by optimizing collections of trees for both individually accurate and collectively diverse predictive behavior. We compare three variants of this QD strategy with two existing ensemble generation strategies over several classification data sets. We then briefly highlight the effect of the evolutionary algorithm at the core of the strategy. The examined algorithms generate ensembles with distinct predictive behaviors as measured by classification accuracy and intrinsic diversity. The plotted behaviors hint at highly data-dependent relationships between these metrics. QD-based strategies are suggested as a means to optimize classifier ensembles along this performance curve along with other suggestions for future work.