A contracts theory embeds non-monotonic composition (with respect to implementation) if the fact that a composition of two components implements a specification $$\mathcal {S}$$ does not generally follow from one of these components implementing $$\mathcal {S}$$. In contrast to monotonic composition, non-monotonic composition offers the additional expressiveness of specifying properties that only hold locally for a component since non-monotonic composition does not enforce all properties to be preserved when composing. Despite that this additional expressiveness is clearly needed, it implies that cases where monotony is indeed desired needs to be managed explicitly. The present paper elaborates on this topic by introducing a contracts theory embedding non-monotonic composition, and exploring conditions for ensuring monotonic composition in the context of this theory.