We extend an earlier interferometric synthetic aperture radar (InSAR) survey covering about 900 remote volcanos of the central Andes (14¿--27¿S) between the years 1992 and 2002. Our survey reveals broad (10s of km), roughly axisymmetric deformation at 4 volcanic centers: two stratovolcanoes are inflating (Uturuncu, Bolivia, and Hualca Hualca, Peru); another source of inflation on the border between Chile and Argentina is not obviously associated with a volcanic edifice (here called Lazufre); and a caldera (Cerro Blanco, also called Robledo) in northwest Argentina is subsiding. We explore the range of source depths and volumes allowed by our observations, using spherical, ellipsoidal and crack-like source geometries. We further examine the effects of local topography upon the deformation field and invert for a spherical point-source in both elastic half-space and layered-space crustal models. We use a global search algorithm, with gradient search methods used to further constrain best-fitting models. Inferred source depths are model-dependent, with differences in the assumed source geometry generating a larger range of accepted depths than variations in elastic structure. Source depths relative to sea level are: 8--18 km at Hualca Hualca; 12--25 km for Uturuncu; 5--13 km for Lazufre, and 5--10 km at Cerro Blanco. Deformation at all four volcanoes seems to be time-dependent, and only Uturuncu and Cerro Blanco were deforming during the entire time period of observation. Inflation at Hualca Hualca stopped in 1997, perhaps related to a large eruption of nearby Sabancaya volcano in May 1997, although there is no obvious relation between the rate of deformation and the eruptions of Sabancaya. We do not observe any deformation associated with eruptions of Lascar, Chile, at 16 other volcanoes that had recent small eruptions or fumarolic activity, or associated with a short-lived thermal anomaly at Chiliques volcano. We posit a hydrothermal system at Cerro Blanco to explain the rate of subsidence there. For the last decade, we calculate the ratio of the volume of magma intruded to extruded is between 1--10, and that the combined rate of intrusion and extrusion is within an order of magnitude of the inferred geologic rate.