We would like to thank the members of the committee for the third International Planning Competition. In particular, discussions with Drew McDermott, Fahiem Bacchus, David Smith and Hector Geffner in turns infuriated, intrigued and delighted us and contributed immeasurably to the strengths of this paper. Many others have offered comments and insights that have allowed us to develop the work we present here. We would like to thank Jörg Hoffmann, Malte Helmert, Antonio Garrido, Stefan Edelkamp, Nicola Muscettola, Mark Boddy, Keith Golden, Jeremy Frank, Ari Jónsson, Julie Porteous, Alex Coddington, Stephen Cresswell, Luke Murray, Keith Halsey and Richard Howey for the many helpful discussions we have shared.