Mycorrhizas play a pivotal role in phosphorus (P) acquisition of plant roots, by enhancing the soil volume that can be explored. Non-mycorrhizal plant species typically occur either in relatively fertile soil or on soil with a very low P availability, where there is insufficient P in the soil solution for mycorrhizal hyphae to be effective. Soils with a very low P availability are either old and severely weathered or relatively young with high concentrations of oxides and hydroxides of aluminium and iron that sorb P. In such soils, cluster roots and other specialised roots that release P-mobilising carboxylates are more effective than mycorrhizas. Cluster roots are ephemeral structures that release carboxylates in an exudative burst. The carboxylates mobilise sparingly-available sources of soil P. The relative investment of biomass in cluster roots and the amount of carboxylates that are released during the exudative burst differ between species on severely weathered soils with a low total P concentration and species on young soils with high total P concentrations but low P availability. Taking a modelling approach, we explore how the optimal cluster-root strategy depends on soil characteristics, thus offering insights for plant breeders interested in developing crop plants with optimal cluster-root strategies.