Abstract. Usage of combinatorial testing is wide spreading as an effective technique to reveal unintended feature interaction inside a given system. To this aim, test cases are constructed by combining tuples of assignments of the different input parameters, based on some effective combinatorial strategy. The most commonly used strategy is two-way (pairwise) coverage, requiring all combinations of valid assignments for all possible pairs of input parameters to be covered by at least one test case. In this paper a new heuristic strategy developed for the construction of pairwise covering test suites is presented, featuring a new approach to support expressive constraining over the input domain. Moreover, it allows the inclusion or exclusion of ad-hoc combinations of parameter bindings to let the user customize the test suite outcome. Our approach is tightly integrated with formal logic, since it uses test predicates to formalize combinatorial testing as a logic problem, and applies an e...