On 2008 May 29 an earthquake doublet shook the southwestern part of Iceland. The first main shock originated beneath Mt Ingólfsfjall, located near the western margin of the South Iceland Seismic Zone (SISZ) approximately 40 km east of the capital Reykjavík. Immediate aftershock activity was recorded by the SIL seismic network, operated by the Icelandic Meteorological Office (IMO), with both N-S and E-W structures illuminated over a broad area. A continuous GPS (CGPS) network, also operated by the IMO, recorded coseismic offsets with up to 200 mm of horizontal motion at the closest stations. We estimate the coseismic surface deformation observed by campaign and continuous GPS and satellite radar data (InSAR). We invert the geodetic data to find the optimal geometry, location and slip on the main faults, accounting for variation in the elastic parameters of the crust with depth. Our models indicate that most of the slip occurred on two N-S structures spaced ~5 km apart. From a joint inversion of GPS and InSAR data for variable slip models we find that most of the slip for the first (Ingólfsfjall) event was concentrated at 2-4 km depth with a maximum of 1.9 m, whereas the slip on the second (Kross) fault was located deeper, at 3-6 km depth with up to 1.4 m of motion. The models give similar geodetic moments for the two main events, equivalent to a moment magnitude of Mw5.8 and Mw5.9 for the first and second event, respectively. Our estimated composite moment therefore equals a Mw6.1 for the doublet, smaller than the Mw6.3 estimated from teleseismic data (e.g. NEIC and Harvard). The geodetic data support rupture on two main faults and analysis of high-rate (1Hz) CGPS data suggests that slip on the second fault initiated within 3 s of the first main shock. Static Coulomb failure stress calculations indicate that the first event caused a stress increase in the area of the main asperity (i.e. at the location of the largest slip patch) on the second fault. However, we cannot rule out dynamic stress triggering due to the short time between the two main events. The 2008 May 29 earthquake doublet appears to be a continuation of the earthquake sequence that started in 2000 June, when two Mw6.5 events struck the eastern and central part of the South Iceland Seismic Zone, in the span of 81 hr. The 2000 June-2008 May sequence has released about half of the moment accumulated by plate motion since the previous earthquake sequence in 1896-1912. Therefore, continued earthquake activity with moderate size events rupturing N-S faults in the SISZ in the coming decades is likely.