Populations often exhibit a pronounced degree of individual variability and this can be important when constructing ecological models. In this paper, we revisit the role of inter-individual variability in population persistence and stability under predation pressure. As a case study, we consider interactions between a structured population of zooplankton grazers and their predators. Unlike previous structured population models, which only consider variability of individuals according to the age or body size, we focus on physiological and behavioural structuring. We first experimentally demonstrate a high degree of variation of individual consumption rates in three dominant species of herbivorous copepods (Calanus finmarchicus, Calanus glacialis, Calanus euxinus) and show that this disparity implies a pronounced variation in the consumption capacities of individuals. Then we construct a parsimonious predator-prey model which takes into account the intra-population variability of prey individuals according to behavioural traits: effectively, each organism has a 'personality' of its own. Our modelling results show that structuring of prey according to their growth rate and vulnerability to predation can dampen predator-prey cycles and enhance persistence of a species, even if the resource stock for prey is unlimited. The main mechanism of efficient top-down regulation is shown to work by letting the prey population become dominated by less vulnerable individuals when predator densities are high, while the trait distribution recovers when the predator densities are low.