The notion of a level of consciousness is a key construct in the science of consciousness. Not only is the term employed to describe the global states of consciousness that are associated with post-comatose disorders, epileptic absence seizures, anaesthesia, and sleep, it plays an increasingly influential role in theoretical and methodological contexts. However, it is far from clear what precisely a level of consciousness is supposed to be. This paper argues that the levels-based framework for conceptualizing global states of consciousness is untenable and develops in its place a multidimensional account of global states.