Efficient and reliable detection of radiological or nuclear threats is a crucial part of national and international efforts to prevent terrorist activities. Radiation Portal Monitors (RPMs), which are deployed worldwide, are intended to interdict smuggled fissile material by detecting emissions of neutrons and gamma rays. However, considering the range and variety of threat sources, vehicular and shielding scenarios, and that only a small signature is present, it is important that the design of the RPMs allows these signatures to be accurately differentiated from the environmental background. Using Monte-Carlo neutron-transport simulations of a model helium-3 detector system we have conducted a parameter study to identify the optimum combination of detector shielding, moderation, and collimation that maximises the sensitivity of neutronsensitive RPMs. These structures, which could be simply and cost-effectively added to existing RPMs, can improve the detector response by more than a factor of two relative to an unmodified, bare design. Furthermore, optimisation of the air gap surrounding the helium tubes also improves detector efficiency.