Many intellectual property protection (IPP) techniques have been proposed. Their primary objectives are providing convincible proof of authorship with least degradation of the quality of the intellectual property (IP), and achieving robustness against attacks. These are also well accepted as the most important criteria to evaluate different IPP techniques. The essence of such techniques is to limit the solution space by embedding signatures as constraints. One key issue that should be addressed but has not been discussed is the fairness of the techniques: what is the quality of the solution subspace for different signatures, that is, how large the solution subspace is (uniqueness), and how difficulty it is to get a solution from such subspace (hardness)? In this paper, we introduce fairness as one of the metrics for good IPP techniques and post the challenge problem of how to design fair watermarking techniques. We claim that all fair techniques have to be instance-oriented and due to the complexity of the problem itself, we propose an approach that utilizes the statistical information of the problem instance. We use the satisfiability (SAT) problem as an example to illustrate how fairness could be achieved. We make the observation that the unfairness of the previous watermarking techniques comes from the global embedding of the signature and propose fair watermarking techniques. We test the uniqueness and hardness on a model with full knowledge of the solution and real life benchmarks as well. The experimental results show fairness can be achieved.