Recently, belief change within the framework of fragments of propositional logic has gained attention. In the context of revision it has been proposed to refine existing operators so that they operate within propositional fragments, and that the result of revision remains in the fragment under consideration. Later this notion of refinement was generalized to belief change operators. Whereas refinement al- lowed one to define concrete rational operators adapted to propositional fragments in the context of revision and update, it has to be specified for contraction and erasure. We propose a specific notion of refinement for contraction and erasure operators, called reasonable refinement. This allows us to provide refined contrac- tion and erasure operators that satisfy the basic postulates. We study the logical properties of reasonable refinement of two model-based contraction operators and two model-based erasure operators. Our approach is not limited to the Horn frag- ment but applicable to many fragments of propositional logic, like Krom and affine fragments