  We elucidate the structure of the next-to-leading-power soft-gluon expansion
of arbitrary one-loop massless-QCD amplitudes. The expansion is given in terms
of universal colour-, spin- and flavour-dependent operators acting on
process-dependent gauge-invariant amplitudes. The result is proven using the
method of expansion-by-regions and tested numerically on non-trivial processes
with up to six partons. In principle, collinear-region contributions are
expressed in terms of convolutions of universal jet operators and
process-dependent amplitudes with two collinear partons. However, we evaluate
these convolutions exactly for arbitrary processes. This is achieved by
deriving an expression for the next-to-leading power expansion of tree-level
amplitudes in the double-collinear limit, which is a novel result as well.
Compared to previous studies, our analysis, besides being more general, yields
simpler formulae that avoid derivatives of process-dependent amplitudes in the
collinear limit.
