Evolutionary biologists typically predict future evolutionary responses to natural selection by analysing evolution on an adaptive landscape. Much theory assumes symmetric fitness surfaces even though many stabilizing selection gradients deviate from symmetry. Here we revisit Landes adaptive landscape and introduce novel analytical theory that includes asymmetric selection. Asymmetric selection and the resulting skewed trait distributions bias equilibrium mean phenotypes away from fitness peaks, usually toward the flatter shoulder of the individual fitness surface. We apply this theory to explain a longstanding paradox in biology and medicine: the evolution of excessive defences against enemies. These so-called extraordinary defences can evolve in response to asymmetrical selection when marginal risks of insufficient defence exceed marginal costs of excessive defence. Eco-evolutionary feedbacks between population abundances and asymmetric selection further exaggerate these defences. Recognizing the effect of asymmetrical selection on evolutionary trajectories will improve the accuracy of predictions and suggest novel explanations for apparent sub-optimality.