One of the most important issues concerning the foundations of conscious perception centers on the question of whether perceptual consciousness is rich or sparse. The overflow argument uses a form of 'iconic memory' to argue that perceptual consciousness is richer (i.e., has a higher capacity) than cognitive access: when observing a complex scene we are conscious of more than we can report or think about. Recently, the overflow argument has been challenged both empirically and conceptually. This paper reviews the controversy, arguing that proponents of sparse perception are committed to the postulation of (i) a peculiar kind of generic conscious representation that has no independent rationale and (ii) an unmotivated form of unconscious representation that in some cases conflicts with what we know about unconscious representation.