Mori fibre spaces for K\"ahler threefolds

Let X be a compact Kaehler threefold such that the base of the MRC-fibration has dimension two. We prove that X is bimeromorphic to a Mori fibre space. Together with our earlier result arXiv:1304.4013 this completes the MMP for compact Kaehler threefolds: let X be a non-projective compact Kaehler threefold. Then X has a minimal model or X is bimeromorphic to a Mori fibre space over a non-projective Kaehler surface.