This paper analyses the design of carbon markets in time (i.e., intertemporally). It is part of a twin set of papers that ask, starting from first principles, 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 temporal design that would help to maximise flexibility and to minimise costs, including banking and borrowing and other mechanisms to provide greater carbon price predictability and credibility over time. (C) 2010 Elsevier Ltd. All rights reserved.