Poeppel (2008) observes that there is no clear correspondence between units of analysis in linguistics (especially the abstract and arbitrary-looking principles of syntax) and biological units of neuroscience, concluding that current neurolinguistic research presents a case of cross-sterilization, rather than cross-fertilization. Here the proposal is developed that decomposing syntax into intermediate evolutionary layers, into its evolutionary primitives, not only makes syntax compatible with gradualist accounts, but it also renders it more tangible and less abstract. In this approach, at least some complexities (and oddities) of syntax, such as Subjacency effects and the small clause core, can be seen as side-effects/by-products of evolutionary tinkering. It is conceivable that such evolutionary considerations are a necessary missing ingredient in any attempt to establish links between the postulates of syntax and the units of neuroscience. This article considers concrete linguistic data and suggestions as to where and how to look for neurobiological correlates of syntax.