Testers often represent systems under test in input parameter models. These contain parameters with associated values. Combinations of parameter values, with one value for each parameter, are potential test cases. In most models, some values of two or more parameters cannot be combined. Testers must then detect and avoid or remove these conflicts.This paper proposes two new methods for automatically handling such conflicts and compares these with two existing methods, based on the sizes of the final conflict-free test suites. A test suite reduction method, usable with three of the four investigated methods is also included in the study, resulting in seven studied conflict handling methods.In the experiment, the number and types of conflicts, as well as the size of the input parameter model and the coverage criterion used, are varied. All in all, 3854 test suites with a total of 929, 158 test cases were generated.Two methods stand out as tractable and complementary. The best method (called the avoid methods) with respect to test suite size is to avoid selection of test cases with conflicts. However, this method cannot always be used. The second best method (called the replace method), removing conflicts from the final test suite, is completely general.