  Many collider observables suffer from non-global logarithms not captured by
standard resummation techniques. Classic examples are the light-jet mass event
shape in the limit of small mass and the related hemisphere soft function. We
derive factorization formulas for both of these and explicitly demonstrate that
they capture all logarithms present at NNLO. These formulas achieve full scale
separation and provide the basis for all-order resummations. A characteristic
feature of non-global observables is that the soft radiation is driven by
multi-Wilson-line operators, and the ones arising here map onto those relevant
for the case of narrow-cone jet cross sections. Numerically, the contributions
of non-global logarithms to resummed hemisphere-mass event shapes are sizeable.
