Research into organisation theory contains abundant evidence of the positive effects of ambidexterity on a firm's performance, and of the influence of organisational context on ambidexterity. The present research tests whether organisational context affects innovation ambidexterity. Our results, based on a dataset of 108 large innovative firms, show that firms combining exploration innovation and exploitation innovation should adopt long-term practices that favour risk-taking and creativity, and thereby build an organisational context suited to innovation ambidexterity. Competences were found to have a strong moderating effect. These results have important managerial and theoretical implications. In the case of innovation, firms that simultaneously pursue exploitation and exploration activities should carefully consider how they combine competences and organisational context.