Growth is a critical ecological trait because it can determine population demography, evolution, and community interactions. Predation risk frequently induces decreased foraging and slow growth in prey. However, such strategies may not always be favored when prey can outgrow a predator's hunting ability. At the same time, a growing gape‐limited predator broadens its hunting ability through time by expanding its gape and thereby creates a moving size refuge for susceptible prey. Here, I explore the ramifications of growing gape‐limited predators for adaptive prey growth. A discrete demographic model for optimal foraging/growth strategies was derived under the realistic scenario of gape‐limited and gape‐unconstrained predation threats. Analytic and numerical results demonstrate a novel fitness minimum just above the growth rate of the gape‐limited predator. This local fitness minimum separates a slow growth strategy that forages infrequently and accumulates low but constant predation risk from a fast growth strategy that forages frequently and experiences a high early predation risk in return for lower future predation risk and enhanced fecundity. Slow strategies generally were advantageous in communities dominated by gape‐unconstrained predators whereas fast strategies were advantageous in gape‐limited predator communities. Results were sensitive to the assumed relationships between prey size and fecundity and between prey growth and predation risk. Predator growth increased the parameter space favoring fast prey strategies. The model makes the testable predictions that prey should not grow at the same rate as their gape‐limited predator and generally should grow faster than the fastest growing gape‐limited predator. By focusing on predator constraints on prey capture, these results integrate the ecological and evolutionary implications of prey growth in diverse predator communities and offer an explanation for empirical growth patterns previously viewed to be anomalies.