In service-oriented systems, such as grids and clouds, users are able to outsource complex computational tasks by procuring resources on demand from remote service providers. As these providers typically display highly heterogeneous performance characteristics, service procurement can be challenging when the consumer is uncertain about the computational requirements of its task a priori. Given this, we here argue that the key to addessing this problem is task migration, where the consumer can move a partially completed task from one provider to another. We show that doing this optimally is NP-hard, but we also propose two novel algorithms, based on new and established search techniques, that can be used by an intelligent agent to efficiently find the optimal solution in realistic settings. However, these algorithms require full information about the providers' quality of service and costs over time. Critically, as providers are usually self-interested agents, they may lie strategically about these to inflate profits. To address this, we turn to mechanism design and propose a payment scheme that incentivises truthfulness. In empirical experiments, we show that (i) task migration results in an up to 160% improvement in utility, (ii) full information about the providers' costs is necessary to achieve this and (iii) our mechanism requires only a small investment to elicit this information.