  We present results relevant for the extension of threshold resummation beyond
the next-to-leading logarithmic (NLL) order for QCD hard-scattering processes.
As an example, we consider di-hadron production $H_1 H_2\to h_1 h_2 X$, where
the produced pair has a large invariant mass. Taking into account the
non-trivial color structure of the partonic hard-scattering process, we
determine the hard and soft matrices in color space. In our numerical studies
we find a significant improvement compared to previous results at NLL accuracy.
In particular, the scale dependence of the resummed cross section is greatly
reduced. In addition, we comment on the extension of the techniques developed
in this work to other observables relevant for hadronic collisions.
