This article argues for a task-based approach to identifying and individuating cognitive systems. The agent-based extended cognition approach faces a problem of cognitive bloat and has difficulty accommodating both sub-individual cognitive systems ("scaling down") and some supra-individual cognitive systems ("scaling up"). The standard distributed cognition approach can accommodate a wider variety of supra-individual systems but likewise has difficulties with sub-individual systems and faces the problem of cognitive bloat. We develop a task-based variant of distributed cognition designed to scale up and down smoothly while providing a principled means of avoiding cognitive bloat. The advantages of the task-based approach are illustrated by means of two parallel case studies: re-representation in the human visual system and in a biomedical engineering laboratory.