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Grid programming environments are tools designed to isolate users from issues like heterogeneity, scalability, and adaptability, thus simplifying the use of Grid infrastructure. This paper presents WSPE, a Grid programming environment for Grid-unaware applications. WSPE consists of a simple programming interface and a fully decentralized runtime system following a peer-to-peer organization. WSPE's runtime system employs a new scheduling mechanism, called Round Stealing, inspired on the idea of work stealing. The main focus of this work is to research methods to achieve efficient execution of parallel applications in a Grid computing infrastructure. By simulation, we show that our scheduling mechanism outperforms a more traditional mechanism, in a Grid environment. We also demonstrate how an appropriate choice for a network overlay mechanism can further improve execution efficiency.