The High Energy Jets (HEJ) framework maintains constraints of a full QCD amplitude - such as crossing symmetry, gauge and Lorentz invariance - and adds a leading high energy logarithmic resummation. We recently showed that this leads to an excellent description of measurements at large invariant mass, where approaches without high energy logarithmic considerations fail to obtain a reasonable description. In this talk, I will describe how to include Next-to-Leading-Log corrections to the jet impact current, while maintaining the analytic properties mentioned before. This approach requires the preservation of the full two-jet NLO infrared structure. This ultimately allows for the direct application of standard regularization methods. For HEJ the plan is to utilise the FKS subtraction scheme.