We present TackleTest, an open-source tool for automatic generation of unit-level test cases for Java applications. TackleTest builds on top of two well-known test-generation tools, EvoSuite and Randoop, by adding a new combinatorial-testing-based approach for computing coverage goals that comprehensively exercises different parameter type combinations of the methods under test, at configurable interaction levels. We describe the tool architecture, the main tool components, and the combinatorial type-based testing technique. TackleTest was developed in the context of application modernization at IBM, but it is also applicable as a general-purpose test-generation tool. We have evaluated TackleTest on several IBM-internal enterprise applications as well as on a subset of the SF110 benchmark, and share our findings and lessons learned. Overall, TackleTest implements a new and complementary way of computing coverage goals for unit testing via a novel white-box application of combinatorial testing.