The testing and formal verification of black box software components is a challenging domain. The problem is even harder when specifications of these components are not available. An approach to cope with this problem is to combine testing with learning techniques, such that the learned models of the components can be used to explore unknown implementation and thus facilitate testing efforts. In recent years, we have contributed to this approach by proposing techniques for learning parameterized state machine models and then use them in the integration testing of black box components. The major problem in this technique left unaddressed was the selection of parameter values during the learning process. In this paper, we propose to use an invariant detection mechanism to select values in the learning process, thus refining model inference and testing approach. Initial experiments with small examples yielded positive results.