Web services promise to revolutionise the way computational resources and business processes are offered and invoked in open, distributed systems, such as the Internet. These services are described using machine-readable meta-data, which enables consumer applications to automatically discover and provision suitable services for their workflows at run-time. However, current approaches have typically assumed service descriptions are accurate and deterministic, and so have neglected to account for the fact that services in these open systems are inherently unreliable and uncertain. Specifically, network failures, software bugs and competition for services may regularly lead to execution delays or even service failures. To address this problem, the process of provisioning services needs to be performed in a more flexible manner than has so far been considered, in order to proactively deal with failures and to recover workflows that have partially failed. To this end, we devise and present a heuristic strategy that varies the provisioning of services according to their predicted performance. Using simulation, we then benchmark our algorithm and show that it leads to a 700% improvement in average utility, while successfully completing up to eight times as many workflows as approaches that do not consider service failures.