We analyze in detail a specific 5-dimensional realization of a "brane-universe" scenario where the visible and hidden sectors are localized on spatially separated 3-branes coupled only by supergravity, with supersymmetry breaking originating in the hidden sector. Although general power counting allows order 1/M_{Planck}^2 contact terms between the two sectors in the 4-dimensional theory from exchange of supergravity Kaluza-Klein modes, we show that they are not present by carefully matching to the 5-dimensional theory. We also find that the radius modulus corresponding to the size of the compactified dimension must be stabilized by additional dynamics in order to avoid run-away behavior after supersymmetry breaking and to understand the communication of supersymmetry breaking. We stabilize the radius by adding two pure Yang--Mills sectors, one in the bulk and the other localized on a brane. Gaugino condensation in the 4-dimensional effective theory generates a superpotential that can naturally fix the radius at a sufficiently large value that supersymmetry breaking is communicated dominantly by the recently-discovered mechanism of anomaly mediation. The mass of the radius modulus is large compared to m_{3/2}. The stabilization mechanism requires only parameters of order one at the fundamental scale, with no fine-tuning except for the cosmological constant.

20 pages, LaTeX2e