In 2018, the Organization for Economic Cooperation and Development (OECD) added to their PISA regime the assessment of "global competence". Given this novel, data-driven approach to governing the internationalisation of K-12 education, this study compares this recent intervention to a longer-standing mode of governing for the pedagogical ideals of international education -- the approach of the International Baccalaureate (IB) across its 50-year lifetime. It employs a comparative, critical discursive analysis of how these two influential transnational organisations advance the pedagogical ideals of international education in neoliberal times. It illuminates the history and development of the IB's soft governing for "international mindedness" and the OECD's more recent approach to governing for "global competence" via PISA. As an entity without state authority, the IB has used a regime of centralised examinations for curricular control and quality assurance in the international schools where it was first adopted. However, IB has never attempted to use formal assessment as a direct technique of governing for international mindedness. Arguably, its liberal-humanist foundations and the need for "malleability" of IB across its many sites of adoption has mitigated from taking a too direct approach to its idealist ambitions. Whereas OECD's testing for "global competence" is more ambitious and problematic. Despite the OECD's use of liberal and social-justice vocabulary, its human capital development orientation remains active in its neoliberal conception of global competence. Contrasting these two transnational modalities of governing for the pedagogical ideals of international education, offers insights into the trends and prospects of internationalisation of K-12 education.