Diversity selection is a common task in early drug discovery. One drawback of current approaches is that usually only the structural diversity is taken into account, therefore, activity information is ignored. In this article, we present a modified version of diversity selection, which we term Maximum-Score Diversity Selection, that additionally takes the estimated or predicted activities of the molecules into account. We show that finding an optimal solution to this problem is computationally very expensive (it is NP-hard), and therefore, heuristic approaches are needed. After a discussion of existing approaches, we present our new method, which is computationally far more efficient but at the same time produces comparable results. We conclude by validating these theoretical differences on several data sets.