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Model-based testing has been proposed as a technique to automatically verify that a system conforms to its specification. A popular approach is to use a model-checker to produce a set of test cases by formulating the test generation problem as a reachability problem. To guide the selection of test cases, a coverage criterion is often used. A coverage criterion can be seen as a set of items to be covered, called coverage items. We propose an on-the-fly algorithm that generates a test suite that covers all feasible coverage items. The algorithm returns a set of traces that includes a path fulfilling each item, without including redundant paths. The reachability algorithm explores a state only if it might increase the total coverage. The decision is global in the sense that it does not only regard each individual local search branch in isolation, but the total coverage in all branches together. For simpler coverage criteria as location …