The possibility of introducing small-diameter fibres (interstitial fibres) into the interstices between larger diameter fibres (solvent fibres) to produce continuous interstitial fibre composites (IFCs) has been considered. The interstitial void size and shape is dependent on the type of stacking of the cylindrical fibres. It is shown that the maximum total fibre volume fraction can be substantially increased by the introduction of one or more interstitial fibres. The distribution of the fibre clusters creates a new type of composite microstructure. Possible interstitial fibres and the effect of fibre clusters on composite properties are discussed.