To what extent can the phenomenological character of visual experience be divorced from attention and working memory? Much of Ned Block's recent impressive work can be seen as a sustained argument for accepting a strong dissociation view. Block's view that visual phenomenology overflows cognitive access has been sharply criticized by a group of scientists (e.g. Stan Dehaene and Sid Kouider), who appeal to the so-called "global neuronal workspace model of consciousness". Following Block, I think that much of the controversy can be clarified by examining two experimental paradigms: one designed by George Sperling in 1960 to study iconic memory, the other one called "change blindness" (first reported in the early 1990's). While much of the discussion was first conducted in terms of the binary distinction between phenomenal consciousness and cognitive access, I will argue that it is a mistake to conflate the reportability and the accessibility of a visual experience. I will further examine the problems raised by the recent introduction of the distinction between generic and specific visual phenomenology into the discussion. Finally, I will raise the following puzzle for the overflow view of visual experience: if the visual phenomenology of one's conscious experience can be inaccessible, then whose experience is it? Could a conscious experience be nobody's?