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Current standardization efforts on Web service interoperability provide ways to compose Web services distributed across heterogeneous network environments. Unfortunately, this has been attained at the expense of efficiency, that is, substantial SOAP communication overheads have negative impact on the performance of Web services. To resolve this and improve performance, we have developed a new mechanism for hiding communication latency by means of parallelization of service invocations within a composite Web service. Our mechanism exploits static analysis techniques to keep track of the behavioral states of Web service components through their execution steps and statically detects whether service invocations may have dependencies with each other at certain states. The analysis can thus guarantee the parallelization will not affect the result Of computation. Evaluation shows strong potential of our mechanism: it substantially improves the performance of composite Web services based on a real-world example of Portfolio optimization.