Organisational ambidexterity - the ability of a company to successfully link exploitation and exploration - is a fruitful approach for cross-border management. It is a crucial concept for media companies that, because of the dual (cultural and economic) character of their products, need to reconcile strategies of mere expansion with local customisation when engaging across borders. Drawing on semi-structured interviews with international media managers, this article captures patterns of ambidextrous strategising and organising in cross-border media activities. The article focuses on digitisation, which has altered the opportunities for balancing exploration and exploitation in internationalisation. The analysis reveals how, in this context, exploitation takes centre stage and how patterns of ambidexterity differ significantly depending on the media type and the background of the company.