The majority of efforts to improve admission to master's programmes in Europe for students with a bachelor's from outside the providing university have been focused on standardization of defined outcomes of bachelor's degrees and improvement in mechanisms for recognition of diplomas and degree. With growing diversity within and around these master's programmes, an alternative approach to master's admission is needed. This article analyses the nature and shortcomings of the standardisation and the recognition approach and reports on the creation of a competency-assessment based approach in the Mastermind Europe project. In that project -- part of the EU's ERASMUS+ programme -- Guiding Tools are produced for academic directors of master's programmes (or 'academic masters directors') who want to base their admission decisions less on recognition of a diploma and more on assessment of the applicants' competency. The Guiding Tools focus on specific categories of admission criteria, on how they can be brought together in a coherent framework and on IT tools to help organize the process. The guiding tools are accompanied by a short Introductory Note on the Paradigm Shift from diploma-recognition based to competency-based master's admission. This article is a more elaborate version of that introductory note, reflecting also the progress in thinking and tool development since the start of the project. It is intended both for users of the Guiding Tools who seek more background and detail, and for readers with a general interest in the topic. For users of the Guiding Tools, it may give them additional reasons and arguments that they may find useful to increase commitment in their own university.