  We present predictions for $W^+W^-$ production (with exact decays) that are
next-to-next-to-leading order (NNLO) accurate and consistently matched to a
parton shower. The matching is achieved by upgrading, with MiNLO, the NLO
calculation of $W^+W^- +1$ jet production, in such a way that NLO accuracy is
guaranteed for $W^+W^-$ inclusive observables, and by performing subsequently a
reweighting of the WWJ-MiNLO events, differential in the $W^+W^-$ Born
variables, to the NNLO results obtained with MATRIX.
