  The accuracy of parton-shower simulations is often a limiting factor in the
interpretation of data from high-energy colliders. We present the first
formulation of parton showers with accuracy one order beyond state-of-the-art
next-to-leading logarithms, for classes of observable that are dominantly
sensitive to low-energy (soft) emissions, specifically non-global observables
and subjet multiplicities. This represents a major step towards general
next-to-next-to-leading logarithmic accuracy for parton showers.
