Finding a solution to a Constraint Satisfaction Problem (CSP) is known to be an NP-complete task. This has motivated the multitude of works that have been devoted to developing techniques that simplify CSP instances before or during their resolution. The present work proposes rigidly enforced schemes for simplifying binary CSPs that allow the narrowing of value domains, either via value merging or via value suppression. The proposed schemes can be viewed as parametrized generalizations of two widely studied CSP simplification techniques, namely, value merging and neighbourhood substitutability. Besides, both schemes may be strengthened in order to allow variable elimination, which may result in more significant simplifications. This work contributes also to the theory of tractable CSPs by identifying a new tractable class of binary CSP.