The definition of consciousness as “that which disappears in dreamless sleep and reappears when we wake up or dream” is unsatisfactory. It rules out the possibility of states or phases of dreamless sleep in which some kind of consciousness is present. A strong case for taking seriously this possibility can be constructed by combining resources found in Indian philosophy, Western philosophy of mind, the neuroscience of consciousness, and sleep science. The main message of this paper—besides that of needing to revise the above definition of consciousness—is that we need a more refined taxonomy of sleep states than the one that sleep science and the neuroscience of consciousness currently employ, and that contemplative methods of mind training are relevant for advancing the neurophenomenology of sleep and consciousness.