Combinatorial interaction testing (CIT) is a method to sample configurations of a software system systematically for testing. Many algorithms have been developed that create CIT samples, however few have considered the practical concerns that arise when adding constraints between combinations of options. In this paper, we survey constraint handling techniques in existing algorithms and discuss the challenges that they present. We examine two highly-configurable software systems to quantify the nature of constraints in real systems. We then present a general constraint representation and solving technique that can be integrated with existing CIT algorithms and compare two constraint-enhanced algorithm implementations with existing CIT tools to demonstrate feasibility.