In this paper, we develop a novel algorithm that allows service consumers to execute business processes (or workflows) of interdependent services in a dependable manner within tight time-constraints. In particular, we consider large inter-organisational service-oriented systems, where services are offered by external organisations that demand financial remuneration and where their use has to be negotiated in advance using explicit service-level agreements (as is common in Grids and cloud computing). Here, different providers often offer the same type of service at varying levels of quality and price. Furthermore, some providers may be less trustworthy than others, possibly failing to meet their agreements. To control this unreliability and ensure end-to-end dependability while maximising the profit obtained from completing a business process, our algorithm automatically selects the most suitable providers. Moreover, unlike existing work, it reasons about the dependability properties of a workflow, and it controls these by using service redundancy for critical tasks and by planning for contingencies. Finally, our algorithm reserves services for only parts of its workflow at any time, in order to retain flexibility when failures occur. We show empirically that our algorithm consistently outperforms existing approaches, achieving up to a 35-fold increase in profit and successfully completing most workflows, even when the majority of providers fail.