Almost all species are subject to continuous attack by parasites and pathogens. Because parasites and pathogens tend to have shorter generation times and often experience stronger selection due to interaction than their victims do, it is frequently argued that they should evolve more rapidly and thus maintain an advantage in the evolutionary race between defence and counter-defence. This prediction generates an apparent paradox: how do victim species survive and even thrive in the face of a continuous onslaught of more rapidly evolving enemies? One potential explanation is that defence is physiologically, mechanically or behaviourally easier than attack, so that evolution is less constrained for victims than for parasites or pathogens. Another possible explanation is that parasites and pathogens have enemies themselves and that victim species persist because parasites and pathogens are regulated from the top down and thus generally have only modest demographic impacts on victim populations. Here we explore a third possibility: that victim species are not as evolutionarily impotent as conventional wisdom holds, but instead have unique evolutionary advantages that help to level the playing field. We use quantitative genetic analysis and individual-based simulations to show that victims can achieve such an advantage when coevolution involves multiple traits in both the host and the parasite.