Monte Carlo simulations are used to evaluate and optimise multiple components of a Compton Suppression System based upon a Broad-energy HPGe primary detector. Several materials for the secondary crystal are evaluated, including NaI(Tl), BGO and LaBr3(Ce). BGO was found to be the most effective across the required energy range, with the sizes of the proposed veto detector then optimised to extract the maximum performance for a given volume of material. Suppression factors are calculated for a range of nuclides (both single and cascade emitters) with improvements of 2 for the Compton Suppression Factors, and 10 for the continuum reduction when compared to the Compton suppression system currently in use. This equates to a reduction in the continuum by up to a factor of similar to 240 for radionuclides such as Co-60, which is crucial for the detection of low-energy, low-activity gamma emitters typically swamped by such a continuum. Crown Copyright (C) 2014 Published by Elsevier B.V. All rights reserved.