Philosophers often discuss zombies and inverts, hypothetical cases in which perfect physical/functional duplicate of us either lack conscious experience or else have their experiences “shuffled” such that they correlate with different stimuli and physiological states. The idea that there may also be physical/functional duplicates of us who have more kinds of experiences than we do, however, has gone unnoticed. These phenomenal smugglers, as I call them, raise novel questions on what sorts of restrictions there may be on how many or what sorts of extra experiences our smuggler counterparts could conceivably have. I appeal to the dimensional structure, the precision structure, the combinatorial structure, the syntactic structure, and the integration structure of consciousness in order to clarify and answer the questions raised by smugglers about the conceivable upper bounds of consciousness.