Testing is a widely-used method to assess software quality. Coverage criteria and coverage measurements are used to ensure that the constructed test-suites adequately test the given software. Since manually developing such test-suites is too expensive in practice, various automatic test-generation approaches were proposed - all of them having different strengths and weaknesses. In the past, specific approaches were combined to compensate weaknesses. While verification techniques, like symbolic execution, are used to generate tests, they are rarely combined for addressing the same problem. We present CoVeriTest, a hybrid system for test-case generation, which iteratively combines verifiers that apply reachability analyses. Thereby, it allows to adjust the level of cooperation and to assign individual time budgets per verifier. In our experiments, we combine explicit-state model checking and predicate abstraction to systematically study different CoVeriTest configurations. Moreover, CoVeriTest achieves higher coverage than state-of-the-art test-generation tools for some programs.