Natural selection does not lead to optimal solutions due to trade-offs and environmental variation, genetic and developmental constraints, and historical contingency. In this paper we propose that constraints like these also often apply to the improvement of both crop varieties and management practices, creating a dual biological and agronomic barrier for the optimisation of crops. We discuss constraints on optimisation of 1) crop ancestors, by natural selection, 2) crop traits, by artificial selection and biotechnology, and 3) crop management. We outline how trade-offs and environmental variation make single-factor optimisation (e.g. "optimum leaf angle" or "optimal fertiliser rate") impossible. Definitions of "optimal" that recognise trade-offs and variability can help, but we argue there are major constraints on even those forms of optimality. Optimality theory may be useful to formulate null hypotheses, however, as divergence between actual traits and theoretical optima can highlight constraints that are biologically interesting and agronomically relevant. Understanding the nature and size of these constraints can help us map more likely pathways for future improvements in agriculture.