We present the analysis of the 1/Q-suppressed non-perturbative (NP) contribution to the cumulative out-of-event-plane momentum distribution in e+e- annihilation in the near-to-planar three-jet region. It complements our previous study of the perturbative (PT) distributions resummed to single logarithmic accuracy. Due to inter-jet soft gluon radiation, the NP contributions (as well as the PT distributions) are sensitive to the geometry (the angles between jets) and the colour structure of the ...