One decade ago, researchers using event-related brain potential (ERP) measurements stumbled upon what looked like a Semantic Illusion in language comprehension: Semantically anomalous, but otherwise well-formed sentences did not affect the meaning-related N400 component, but instead increased the amplitude of the structure-related P600 component. This finding spawned five new models of language comprehension, all of which claim that instead of a single comprehension process, there are two or even more separate processing streams, one of which is not driven by structure, but by word meaning alone. Here, we will argue that there is a much simpler way to account for these data, and we will present evidence from neurocomputional simulations showing that our alternative explanation is able to predict all relevant ERP patterns found in the literature.