  A novel way of computing high-order amplitudes in the multi-Regge limit of
planar maximally supersymmetric Yang-Mills theory is presented. In this
framework, we are able to obtain high-loop and high-leg results by an easy
operation on known amplitudes with fewer loops and lower multiplicity. This
mechanism will be reviewed, along with an ensuing factorisation which allows us
to determine leading logarithmic MHV results for any number of legs at a fixed
loop order.
