This paper reports the findings of a study of the filler content required in concrete to produce a minimum voids ratio (or maximum packing density) according to particle packing models. The calculation of theoretical voids ratio shows that the filler content required to minimise voids ratio depends on the original concrete mix proportions as well as the fineness of the fillers. Concrete mixes with a high original cement content required the inclusion of finer filler to minimise the voids ratio and coarser, low-cost fillers were suitable for mixes with lower cement contents. The study shows the importance of both filler fineness and mix proportions on minimising voids ratio at a cement-sized grain level. Agglomeration of the fine particles and an effective utilisation of filler are also considered and two criteria are proposed to determine the filler content required to minimise the voids ratio in concrete.