In a recent article in this Journal, Fumagalli argues that economists are provisionally justified in resisting prominent calls to integrate neural variables into economic models of choice. In other articles, various authors engage with Fumagalli’s argument and try to substantiate three often-made claims concerning neuroeconomic modelling. First, the benefits derivable from neurally informing some economic models of choice do not involve significant tractability costs. Second, neuroeconomic modelling is best understood within Marr’s three-level of analysis framework for information-processing systems. And third, (...) neural findings enable choice modellers to confirm the causal relevance of variables posited by competing economic models, identify causally relevant variables overlooked by existing models, and explain observed behavioural variability better than standard economic models. In this paper, I critically examine these three claims and respond to the related criticisms of Fumagalli’s argument. Moreover, I qualify and extend Fumagalli’s account of how trade-offs between distinct modelling desiderata hamper neuroeconomists’ attempts to improve economic models of choice. I then draw on influential neuroeconomic studies to argue that even the putatively best available neural findings fail to substantiate current calls for a neural enrichment of economic models. (shrink)