Consciousness supervenes on activity; computation supervenes on structure. Because of this, some argue, conscious states cannot supervene on computational ones. If true, this would present serious difficulties for computationalist analyses of consciousness (or, indeed, of any domain with properties that supervene on actual activity). I argue that the computationalist can avoid the Superfluous Structure Problem (SSP) by moving to a dispositional theory of implementation. On a dispositional theory, the activity of computation depends entirely on changes in the intrinsic properties of (...) implementing material. As extraneous structure is not required for computation, a system can implement a program running on some but not all possible inputs. Dispositional computationalism thus permits episodes of computational activity that correspond to potential episodes of conscious awareness. The SSP cannot be motivated against this account, and so computationalism may be preserved. (shrink)