© 2016, The Author(s). We present a simulation program for the production of a pair of W bosons in association with a jet, that can be used in conjunction with general-purpose shower Monte Carlo generators, according to the Powheg method. We have further adapted and implemented the Minlo′method on top of the NLO calculation underlying our W+W−+ jet generator. Thus, the resulting simulation achieves NLO accuracy not only for inclusive distributions in W+W−+ jet production but also W+W−production, i.e. when the associated jet is not resolved, without the introduction of any unphysical merging scale. This work represents the first extension of the Minlo′method, in its original form, to the case of a genuine underlying 2 → 2 process, with non-trivial virtual corrections.