We construct an expression for the n-point one-loop graviton scattering amplitude with a single negative helicity external leg using an augmented recursion technique. We analyse the soft-limits of these amplitudes and demonstrate that they have soft behaviour beyond the conjectured universal behaviour.

We consider the factorisation of one-loop amplitudes at complex kinematic points. By determining the terms that are absent for real kinematics, we can construct a recursive ansatz for the purely rational pieces of one-loop amplitudes in massless theories. We illustrate this method by verifying the Bern et.al. n-point ansatze for the single-minus one-loop amplitudes in Yang-Mills theory and by constructing the scalar contribution to the one-loop five graviton MHV scattering amplitude.