Near-to-planar three-jet events at NNLL accuracy

We extend the ARES method for next-to-next-to-leading-logarithmic (NNLL) QCD resummations to three-jet event shapes in e+e- collisions in the near-to-planar limit. In particular, we define a NNLL radiator for three hard emitters, and discuss new features of NNLL corrections arising specifically in this case. As an example, we present predictions for the D-parameter, matched to exact next-to-leading order (NLO). After inclusion of hadronisation corrections in the dispersive approach, we compare our predictions with LEP1 data.