This letter discusses the applicability of boolean satisfiability (SAT) solving to pairwise testing in practice. Due to its recent rapid advance, using SAT solving seems a promising approach for search-based testing and indeed has already been practiced in test generation for pairwise testing. The previous approaches use SAT solving either for finding a small test set in the absence of parameter constraints or handling constraints, but not for both. This letter proposes an approach that uses a SAT solver for constructing a test set for pairwise testing in the presence of parameter constraints. This allows us to make full use of SAT solving for pairwise testing in practice.