In this paper, we propose a modular and fully decentralized protocol to orchestrate fair exchanges between mutually distrustful yet collaborating web services. Our motivation roots in the observation that fair exchange is a key problem in settings where mutually distrustful entities are willing to exchange critical digital items in the absence of a trusted third party, which is typically the case of web services collaborating on a peer-to-peer basis. Examples of such scenarios include multiparty exchanges of security information (e.g., cryptographic keys), multiparty sharing of digital rights (e.g., to display some digital content), digital contract signing, etc. Our fair exchange orchestration protocol is based on two key building blocks, namely a tamperproof secure box and a module solving the well-known Byzantine agreement problem. The tamperproof secure boxes need not communicate directly with each other and are only required in a limited number of key steps of our algorithm. Our approach has the advantage to allow fair exchanges to complete even though truly malicious participants have aborted.