A recurring theme in the literature on technology and organizations is the concept of mirroring, which posits a duality between technological and organizational design decisions. In this paper we highlight a second, orthogonal duality between components and interfaces: designers of both products and organizations must decide what information to hide within component boundaries and what to expose to other designers. Although the component-interface duality appears in many settings, it presents especially vexing strategic challenges in the design and production of complex digital artifacts. We present a typology of four interlinked perspectives on these kinds of strategic design problems, and discuss the tensions that can arise between them. We conjecture that the ability to resolve these tensions may be a significant and underappreciated source of competitive advantage, and suggest future empirical research that could use this typology to develop new ways of thinking about architectural strategy in IT-intensive industries.