GUI testing is a form of system testing where test cases are based on user interactions. A user interaction may be encoded by a sequence of events (e.g., mouse clicks) together with input data (e.g., string values for text boxes). For selecting event sequences, one can use the black-box approach based on Event Flow Graphs. For selecting input data, one can use the white-box approach based on parameterized unit tests and symbolic execution. The contribution of this paper is an approach to make the principle of parameterized unit testing available to black-box GUI testing. The approach is based on the new notion of parameterized GUI tests. We have implemented the approach in a new tool. In order to evaluate whether parameterized GUI tests have the potential to achieve high code coverage, we apply the tool to four open source GUI applications. The results are encouraging.