Summary. When using computer models to provide policy support it is normal to encounter ensembles that test only a handful of feasible or idealized decision scenarios. We present a new methodology for performing multilevel emulation of a complex model as a function of any decision within a predefined class that makes specific use of a scenario ensemble of opportunity on a fast or early version of a simulator and a small, well-chosen, design on our current simulator of interest. The method exploits a geometrical approach to Bayesian inference and is designed to be fast, to facilitate detailed diagnostic checking of our emulators by allowing us to carry out many analyses very quickly. Our motivating application involved constructing an emulator for the UK Met Office Hadley Centre coupled climate model HadCM3 as a function of carbon dioxide forcing, which was part of a ‘RAPID’ programme deliverable to the UK Met Office funded by the Natural Environment Research Council. Our application involved severe time pressure as well as limited access to runs of HadCM3 and a scenario ensemble of opportunity on a lower resolution version of the model.