Phage therapy is a promising alternative to traditional antibiotics for treating bacterial infections. Such phage-based therapeutics typically contain multiple phages, but how the efficacy of phage combinations scales with phage richness, identity and functional traits is unclear. Here, we experimentally tested the efficacy of 827 unique phage combinations ranging in phage richness from one to 12 phages. The efficacy of phage combinations increased with phage richness. However, complementarity between functionally diverse phages allowed efficacy to be maximized at lower levels of phage richness in functionally diverse combinations. These findings suggest that phage functional diversity is the key property of effective phage combinations, enabling the design of simple but effective phage therapies that overcome the practical and regulatory hurdles that limit development of more diverse phage therapy cocktails.