'Thick neural event' is introduced to mean an event that requires firings of more than one neuron and a substantive (i.e. additional to merely temporal and spatial) relation among them. It is shown that some well regarded theories (e.g. by Lamme, Koch, etc.) strongly suggest that neural correlates of consciousness (NCCs) are thick neural events. It is then shown that thin (= not thick) neural events provide sufficient causation for neural events leading to behaviour, and that there are good reasons (...) to reject overdetermination by thick events. Thus, any physicalism that recognizes legitimacy of a search for NCCs must either reject theories that embrace thickness of NCCs, or accept the epiphenomenalistic view that the properties in virtue of which we are conscious are not properties in virtue of which events causally contribute to our behaviour. (shrink)