The main objective of this book is to provide solutions to some combinatorial testing issues. The combinatorial testing consists in generating tests that cover all combinations of defined input values. The first issue of this book is that combinatorial testing can generate a large number of tests that are invalid according to the specification of the System Under Test (SUT). These invalid tests are typically those which fail the precondition of system operation. These invalid tests must be discarded from the set of tests used to evaluate the SUT, because they lead to inconclusive verdicts. In our work, combinatorial tests are generated from a test pattern. It is mainly defined as a sequence of operation calls, using a set of values for their parameters. The unfolding of a complex test pattern, where many operation calls and/or input values are used, may be subject to combinatorial explosion, and it is impossible to provide valid tests from the test pattern. This is a second issue of this book.