Enabled by advances in grid and network computing architectures for the delivery of on-demand computing services, the vision of an e-services economy in which computing will be as ubiquitous as a utility is becoming a possibility in business computing. Major firms in the computing industry such as IBM, HP, and SUN Microsystems are focusing on agility and flexibility of computing resources and gearing up for their own versions of on-demand computing and IT outsourcing solutions. Successful business advent of these new computing models requires the development of appropriate pricing mechanisms that are consistent with the enabling technologies. Our paper presents preliminary research in this area, and introduces the notion of contingent auctions to address this lacuna. In contingent auctions, users bid for computing resources in an auction, but are relieved from the contract if demand is not realized. We study different mechanisms — ranging from an advance-commit (capacity reservation) to no-commit (pay-as-you-go) — under such demand uncertainty. We show how the different levels of commitment affect prices, revenues and resource utilization. Our initial results show promise and reiterate the need to address the availability-commitment dichotomy in the design of business models for on-demand computing and IT outsourcing.