SUMMARYAn increasing number of enterprise applications are intensive in their consumption of IT, but are infrequently used. Consequently, organizations either host an oversized IT infrastructure or they are incapable of realizing the benefits of new applications. A solution to the challenge is provided by the large-scale computing infrastructures of Clouds and Grids which allow resources to be shared. A major challenge is the development of mechanisms that allow efficient sharing of IT resources. Market mechanisms are promising, but there is a lack of research in scalable market mechanisms. We extend the Multi-Attribute Combinatorial Exchange mechanism with greedy heuristics to address the scalability challenge. The evaluation shows a trade-off between efficiency and scalability. There is no statistical evidence for an influence on the incentive properties of the market mechanism. This is an encouraging result as theory predicts heuristics to ruin the mechanism's incentive properties.