The decoherence interpretation of quantum measurements is applied to Wigner's friend experiments. A framework in which all the experimental outcomes arise from unitary evolutions is proposed. All the (apparent) wave-function collapses, and the corresponding randomness, result from tracing out relevant parts of the states in which the observers live. The main effect of this framework is ruling out all the inconsistences ensuing from Wigner's friend experiments. Contrary to what is stated in [D. Frauchiger and R. Renner, Quantum theory cannot consistently describe the use of itself, Nat. Comm. 9, 3711 (2018)], this framework makes compatible the conclusions obtained by all the observers. And contrary to what is shown in [C. Bruckner, A no-go theorem for observerindepdendent facts, Entropy 20, 350 (2018)], it makes possible to assign joint truth values to the observations made by all the agents. This framework also narrows down the requisites for such experiments, making virtually impossible to apply them to conscious (human) beings. * armando.relano@fis.ucm.es arXiv:1908.09737v1 [quant-ph]