A closed-system specification models a system in the context of its assumed environment. A component is then a view on the total system, where unnecessary details of other components and the external environment have been abstracted away. Starting from a crude initial model, details of components can be introduced in separate component refinements, and the resulting views can be synthesized by composition into a detailed model of the total system. In contrast to open systems, also component interfaces can be refined in this process. The original model may therefore have abstract interfaces, whose implementability with the available mechanisms is one of the concerns in component refinements. However, since component refinements may then interfere,conditions are needed for their composability. Such conditions are derive in this paper, and the application of component refinements to interface refinement is investigated.