Using ab initio simulations on Fe-Ni-S-C-O-Si liquids, we constrain the origin and composition of the low-velocity layer E′ at the top of Earth's outer core. We find that increasing the concentration of any light element always increases velocity and so a low-velocity and low-density layer (for stability) cannot be made by simply increasing light element concentration. This rules out barodiffusion or simple sedimentation of a light phase for its origin. However, exchanging elements can—depending on the elements exchanged—produce such a layer. We evaluate three possibilities. First, crystalization of a phase from a core may make such a layer, but only if the core contains more than one light element and only if crystalizing phase is very Fe rich. Second, the E′ layer may result from incomplete mixing of an early Earth core with a late impactor, depending on the light element compositions of the impactor and Earth's core. Third, using thermodynamic models for metal-silicate partitioning, we show that a reaction between the core and an FeO-rich basal magma ocean can result in a light and slow layer.