Successful large firms tend to favor incremental innovation at the expense of more radical innovations. Organizational ambidexterity offers organizational designs that are compatible with management of these contradictory forces. However, this literature postulates a balance of these forces without specifying their nature, nor the intensity of their influence. The study of four internal start-ups in charge of the development of innovation breakthrough, within a company dominated by incremental innovations, highlights how some forces are more likely than others to support this type of innovation. This research proposes an in-depth analysis of the balancing mechanisms in highly constrained contexts.