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The United Kingdom will leave the European Union. Brexit will involve many complex negotiations. This article analyses the negotiation position of the parties (UK, EU, Member States) based on a set of four key negotiation factors: agreement options, nonagreement alternatives, interests, and perceptions. A special focus here is on the effect of triggering the formal withdrawal process under the Treaty on European Union’s Article 50 on the non-agreement alternatives of the parties. The article considers the likely negotiation strategy of the UK against this background. It further discusses strategic negotiation moves already made by the parties and moves likely to be made in the future. So far, the parties appear to approach these immensely complex negotiations intuitively, as a zero-sum or even a negative-sum game, engaging only in value-claiming tactics. No neutral process manager is involved so far. Against this background, this article proposes an international, tailor-made mediation process as a means to efficiently steer the withdrawal negotiations and help the parties agree on a value-preserving “withdrawal agreement.