International relations are made up of thick layers of meaning and big streams of data. How can we capture the nuances and scales of increasingly digitalised world politics, taking advantage of the possibilities that come with ‘big data’ and ‘digital methods’ in our discipline of International Relations (IR)? What is needed, we argue, is a methodological twin-move of making big data thick and thick data big. Taking diplomacy, one of IR's core practices as our case, we illustrate how anthropological and computational approaches can be merged in IR research. We report from our experiences with the project DIPLOFACE: Diplomatic Face-Work between Confidential Negotiations and Public Display, investigating how digital communication technologies influence both the study and conduct of age-old and traditionally analogue practices of inter-state diplomacy.