Abstract: Frequently, the design of interactive systems focuses exclusively on the capabilities provided by the dynamic nature of computational media. Yet our have provided many examples in which physical models provide certain strengths not found in computational models. Rather than viewing this as a dichotomy -- where one must choose between one or the other -- we are exploring the creation of computational environments that build on the strengths of combined physical and virtual approaches. Over the last decade, we have developed different design environments to support stakeholders engaged in design processes by enhancing communication, facilitating shared understanding, and creating better artifacts. Until a few years ago, our work explored physical and computational media separately. In this paper we present our efforts to develop integrated design environments linking physical and computational dimensions to attain the complementary synergies that these two worlds offer. Our purpose behind this integration is the development of systems that can enhance the movement from conceptual thinking to concrete representations using face-to-face interaction to promote the negotiation of meaning, the direct interaction with artifacts, and the possibility that diverse stakeholders can participate fully in the process of design. To this end, we analyze the strengths, affordances, weaknesses, and limitations of the two media used separately and illustrate with our most recent work the value added by integrating these environments.