Natural composites achieve damage tolerance through a complex microstructure with several hierarchical levels; this has inspired the development of synthetic composites with hierarchical microstructures, in order to overcome their inherent brittleness. However, while most natural composites have non-self-similar hierarchical microstructures, most synthetic hierarchical designs in the literature use self-similar features. The aim of this work is therefore to investigate whether non-self-similar hierarchical composites could be more damage tolerant than their self-similar equivalent. Non-self-similar hierarchical composites are designed, manufactured and tested; results show that releasing the self-similar constraint can increase the design space of composite microstructures and lead to materials with better damage tolerance, with a clearer warning before failure, and with more stable failure mechanisms.