  We investigate generic properties of one-loop amplitudes in unordered gauge
theories in four dimensions. For such theories the organisation of amplitudes
in manifestly crossing symmetric expressions poses restrictions on their
structure and results in remarkable cancellations. We show that one-loop
multi-photon amplitudes in QED with at least eight external photons are given
only by scalar box integral functions. This QED `no-triangle' property is true
for all helicity configurations and has similarities to the `no-triangle'
property found in the case of maximal N = 8 supergravity. Results are derived
both via a world-line formalism as well as using on-shell unitarity methods. We
show that the simple structure of the loop amplitude originates from the
extremely good BCFW scaling behaviour of the QED tree-amplitude.
