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In this work we study the impact of recent findings regarding non-perturbative corrections in the three-jet region to e+ e− hadronic observables, by performing a simultaneous fit of the strong coupling constant α s and the non-perturbative parameter α 0. We extend the calculation of these power corrections, already known for thrust and C-parameter, to other e+ e− hadronic observables. We find that for some observables the non-perturbative corrections are reasonably well behaved in the two-jet limit, while for others they have a more problematic behaviour. If one limits the fit to the three-jet region and to the well-behaved observables, one finds in general very good results, with the extracted value of α s agreeing well with the world average. This is the case in particular for the thrust and C-parameter for which notably small values of α s have been reported when non-perturbative corrections have been computed using …