We use well-documented time histories of episodic GPS surface deformation and efflux of compressible magma to resolve apparent magma budget anomalies at Soufrière Hills volcano (SHV) on Montserrat, WI. We focus on data from 2003 to 2007, for an inflation succeeded by an episode of eruption-plus-deflation. We examine Mogi-type and vertical prolate ellipsoidal chamber geometries to accommodate both mineralogical constraints indicating a relatively shallow pre-eruption storage, and geodetic constraints inferring a deeper mean-pressure source. An exsolved phase involving several gas species greatly increases andesite magma compressibility to depths >10 km (i.e., for water content >4 wt%, crystallinity ∼40%), and this property supports the concept that much of the magma transferred into or out of the crustal reservoir could be accommodated by compression or decompression of stored reservoir magma (i.e., the “magma-sponge”). Our results suggest quasi-steady deep, mainly mafic magma influx of the order of 2 m3s−1, and we conclude that magma released in eruptive episodes is approximately balanced by cumulative deep influx during the eruptive episode and the preceding inflation. Our magma-sponge model predicts that between 2003 and 2007 there was no evident depletion of magma reservoir volume at SHV, which comprises tens of km3 with radial dimensions of order ∼1–2 km, in turn implying a long-lived eruption.