How can we disentangle the neural basis of phenomenal consciousness from the neural machinery of the cognitive access that underlies reports of phenomenal consciousness? We see the problem in stark form if we ask how we can tell whether representations inside a Fodorian module are phenomenally conscious. The methodology would seem straightforward: Find the neural natural kinds that are the basis of phenomenal consciousness in clear cases – when subjects are completely confident and we have no reason to doubt their authority – and look to see whether those neural natural kinds exist within Fodorian modules. But a puzzle arises: Do we include the machinery underlying reportability within the neural natural kinds of the clear cases? If the answer is “Yes,” then there can be no phenomenally conscious representations in Fodorian modules. But how can we know if the answer is “Yes”? The suggested methodology requires an answer to the question it was supposed to answer! This target article argues for an abstract solution to the problem and exhibits a source of empirical data that is relevant, data that show that in a certain sense phenomenal consciousness overflows cognitive accessibility. I argue that we can find a neural realizer of this overflow if we assume that the neural basis of phenomenal consciousness does not include the neural basis of cognitive accessibility and that this assumption is justified (other things being equal) by the explanations it allows.