The dorsoventral axis of the Drosophila embryo is patterned by a gradient of bone morphogenetic protein (BMP) ligands. In a process requiring at least three additional extracellular proteins, a broad domain of weak signaling forms and then abruptly sharpens into a narrow dorsal midline peak. Using experimental and computational approaches, we investigate how the interactions of a multiprotein network create the unusual shape and dynamics of formation of this gradient. Starting from observations suggesting that receptor-mediated BMP degradation is an important driving force in gradient dynamics, we develop a general model that is capable of capturing both subtle aspects of gradient behavior and a level of robustness that agrees with in vivo results.