This study compares seven different methods for handling constraints in input parameter models when using combination strategies to select test cases. Combination strategies are used to select test cases based on input parameter models. An input parameter model is a representation of the input space of the system under test via a set of parameters and values for these parameters. A test case is one specific combination of values for all the parameters. Sometimes the input parameter model may contain parameters that are not independent. Some sub-combinations of values of the dependent parameters may not be valid, i.e., these sub-combinations do not make sense. Combination strategies, in their basic forms, do not take into account any semantic information. Thus, invalid sub-combinations may be included in test cases in the test suite. This paper proposes four new constraint handling methods and compares these with three existing methods in an experiment in which the seven constraint handling methods are used to handle a number of different constraints in different sized input parameter models under three different coverage criteria. All in all, 2568 test suites with a total of 634,263 test cases have been generated within the scope of this experiment.