This study explores the decision-facilitating role of performance measurement systems (PMSs) in firms attempting to translate competence ambidexterity (i.e., the simultaneous pursuit of exploration and exploitation) into innovation ambidexterity outcomes (i.e., the achievement of both radical and incremental innovations). Drawing on paradox and organisational conflict literature, this study emphasises the role of cognitive conflict, generated by PMSs, in shaping the relationships between competence ambidexterity and innovation ambidexterity. Based on survey data from a sample of 90 Irish firms, our findings indicate that competence ambidexterity is associated with (a) the choice to have a balanced set of performance measures, and (b) the use of PMSs for frequent and intensive debate between top managers. Furthermore, the study reveals that these choices are interdependent, as they function as complements in generating cognitive conflict, which in turn drives the realisation of innovation ambidexterity outcomes. The results also show that cognitive conflict is not directly associated with the development of competence ambidexterity, but is instead generated through the conjoint action of a balanced PMS design and the use of PMSs for intensive debate. Overall, this study demonstrates the interdependent nature of choices concerning the design and use of PMSs, and the significant role of PMSs as generators of cognitive conflict in firms attempting to achieve ambidexterity.