The weak-coupling expansion of QCD high-energy scattering fails near kinematic thresholds due to the restricted phase space for real emission. The logarithmic enhancements in the kinematic variable that characterizes the threshold must be resummed to all orders in the coupling expansion to arrive at a reliable approximation. The leading power logarithms are well-known and can be summed to the next-to-next-to-next-to-leading logarithmic order. In contrast, much less is understood at next-to-leading power. We derive a threshold resummation formula at next-to-leading power employing the soft-collinear effective theory. The anomalous dimensions of subleading-power soft functions are calculated directly. As a result, we resum the leading logarithms near the kinematic threshold. Expansion of the resummed result leads to the leading logarithms at fixed orders, providing new results at the five-loop order and beyond.
