  We present two novel results about the universal structure of radiative QED
amplitudes in the soft and in the collinear limit. On the one hand, we extend
the well-known Low-Burnett-Kroll theorem to the one-loop level and give the
explicit relation between the radiative and non-radiative amplitude at
subleading power in the soft limit. On the other hand, we consider a
factorisation formula at leading power in the limit where the emitted photon
becomes collinear to a light fermion and provide the corresponding one-loop
splitting function. In addition to being interesting in their own right these
findings are particularly relevant in the context of fully-differential
higher-order QED calculations. One of the main challenges in this regard is the
numerical stability of radiative contributions in the soft and collinear
regions. The results presented here allow for a stabilisation of real-virtual
amplitudes in these delicate phase-space regions by switching to the
corresponding approximation without the need of explicit computations.
