  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 NLO. After inclusion of hadronisation corrections in the dispersive
approach, we compare our predictions with LEP1 data.
