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We present a lightweight Byzantine fault tolerance (BFT) algorithm, which can be used to render the coordination of web services business activities (WS-BA) more trustworthy. The lightweight design of the BFT algorithm is the result of a comprehensive study of the threats to the WS-BA coordination services and a careful analysis of the state model of WS-BA. The lightweight BFT algorithm uses source ordering, rather than total ordering, of incoming requests to achieve Byzantine fault tolerant, state-machine replication of the WS-BA coordination services. We have implemented the lightweight BFT algorithm, and incorporated it into the open-source Kandula framework, which implements the WS-BA specification with the WS-BA-I extension. Performance evaluation results obtained from the prototype implementation confirm the efficiency and effectiveness of our lightweight BFT algorithm, compared to traditional BFT techniques.