For inclusive enough processes, the structure of unfactorized parsonic cross sections, together with constraints from mass-factorization theorems, allows the resummation of logarithms beyond the leading power. I present the application of this method to the off-diagonal parsonic cross section of inclusive Higgs production and Drell-Yan, as well as to the off-diagonal splitting functions and the corresponding coefficient functions in inclusive deep-inelastic scattering and semi-inclusive electron-positron annihilation.