Is it possible to talk accurately about unintended double non-taxation and aggressive tax planning from an international perspective? Do they have an international meaning? The aim of this contribution is to clarify the meaning of unintended double non-taxation and aggressive tax planning in the international debate. When it comes to intentions, this contribution proposes splitting the concept of double non-taxation into proper double non-taxation and twice non-taxation. Proper double non-taxation provides the dividing line between intended and unintended double non-taxation at treaty level. The parallel exercise of sovereignty by different states leading to non-taxation from a domestic perspective and then to double non-taxation across borders relates to twice non-taxation, situations where it is not possible to infer intentions in the abstract out of that very outcome. One of the main conclusions of the article lies on the national nature of the concepts of aggressive tax planning and unintended double non-taxation present in the international tax debate and the relation between them, denying their international character. Aggressive tax planning is defined by those domestic and treaty measures that identify and deter those outcomes that are considered non-acceptable or unintended in advance, where avoidance is not present whatsoever. This contribution grounds its conclusions through the analysis of double non-taxation stemming from sovereignty and the confrontation of state behaviour and taxpayer behaviour with respect to the relevant outcome of double non-taxation, paying great attention not only to tax planning and avoidance but also to tax competition.