This paper provides a formal model for the burden of persuasion in dialogues, and in particular, in legal proceedings. The model shows how an allocation of the burden of persuasion may induce single outcomes in dialectical contexts in which, without such an allocation, the status of conflicting arguments would remain undecided. Our approach is based on a two-stage labelling. The first-stage labelling determines what arguments are accepted, rejected or undecided, regardless of the allocation of burden. The second-stage labelling revises the dialectical status of first-stage undecided arguments, according to burdens of persuasion. The labelling is finally extended in such a way as to obtain a complete labelling. Our model combines two ideas that have emerged in the debate on the burden of persuasion: the idea that the burden of persuasion determines the solution of conflicts between arguments, and the idea that its satisfaction depends on the dialectical status of the arguments concerned. Our approach also addresses inversions of the burden of persuasion, namely, cases in which the burden of persuasion over an argument does not extend to its subarguments.