•Shortfall in the EDGE2D-EIRENE simulated JET divertor radiated power studied.•Atomic and molecular electron power loss terms independently scaled in EIRENE.•Strong sensitivity found to the atomic electron power loss term.•Allows access to lower temperature divertor parameter space.•EDGE2D-EIRENE simulations include D2 molecular radiation for the first time. A discrepancy in the divertor radiated powers between EDGE2D-EIRENE simulations and JET-ILW experiments employing a set of NBI-heated L-mode discharges with step-wise density variation is investigated. The analysis shows the importance of the contributions from the deuterium fuel to the divertor radiated power, making these discharges ideal for this study. Molecular radiation losses from D2 molecules have been included for the first time and the present simulations allow the atomic and molecular electron power loss terms in EIRENE to be independently scaled in order to understand their importance in determining the simulated electron temperatures and distribution of radiated power.