The pressure to innovate is growing as technology cycles change more rapidly. Organisations need to balance exploration and exploitation effectively if they are to heed the innovation imperative. Organisational ambidexterity is proposed as a means to achieve such balance with structural or contextual ambidexterity as possible choices. Yet how organisations become ambidextrous is an as yet under-researched area, and different industry sectors may pose different innovation challenges. Using the case study method, this paper examines how a computer games company responds to an industry-specific innovation challenge and how it endeavours to balance exploration and exploitation. The findings suggest that ambidexterity is difficult to achieve, and is fraught with organisational tensions which might eventually jeopardise the innovation potential of a company. The paper suggests that more qualitative research is needed to further our understanding of innovation challenges, innovation management and organisational ambidexterity.