This paper analyses the design of carbon markets in space (i.e., geographically). It is part of a twin set of papers that, starting from first principles, ask what an optimal global carbon market would look like by around 2030. Our focus is on firm-level cap-and-trade systems, although much of what we say would also apply to government-level trading and carbon offset schemes. We examine the "first principles" of spatial design to maximise flexibility and to minimise costs, including key design issues in linking national and regional carbon markets together to create a global carbon market. (C) 2010 Elsevier Ltd. All rights reserved.