Ground surface tilts recorded proximal to a growing lava dome, and sustained through repeated dome collapses, provide unique geodetic constraints on the depth, size, and overpressures of the shallow magmatic system at Soufri¿re Hills Volcano. Tilt records identify a single pressure-source inflating with periods ~3--30 h. Sustained tilt amplitude ratios for paired stations identify the pressure-source at a centroid depth between ~740 and 970 m. This pressure-source and its robust oscillatory response survived a dome collapse that removed the upper ~200 m of the magmatic system. Shallow overpressures of 1--4 MPa are confirmed over a radius of 200--340 m; this size suggests pressurization of a fluid-saturated fractured rock mass annulus surrounding a narrow magma conduit.