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Search-based test case generation for object-oriented software is hindered by the size of the search space, which encompasses the arguments to the implicit and explicit parameters of the test object's public methods. The performance of this type of search problems can be enhanced by the definition of adequate Input Domain Reduction strategies. The focus of our on-going work is on employing evolutionary algorithms for generating test data for the structural unit-testing of Java programs. Test cases are represented and evolved using the Strongly-Typed Genetic Programming paradigm; Purity Analysis is particularly useful in this situation because it provides a means to automatically identify and remove Function Set entries that do not contribute to the definition of interesting test scenarios.