SUMMARY Standard data and methods, such as the inversion of seismic and GPS data, have been used extensively to infer the details of the 2004 December 26 earthquake. The unprecedented large size of this event gave the opportunity to modern altimeters to provide the first clear records of a tsunami in deep ocean, therefore allowing us to study the rupture history from an independent perspective. We invert the Jason-1 and Topex–Poseidon altimetry records, considering the new constraints available on the geometry of the fault plane, and taking them into account in a 3-D rupture model. The data are corrected for the non-negligible effect of satellite motion during measurements. Our results show that the rupture propagated over the 1500 km of subduction zone initially identified by the aftershock distribution, with a magnitude of Mw= 9.1. Our solution compares well with the latitudinal distribution of slip inferred from other data sets, with a maximum of energy release north of Sumatra, and two other slip patches near the Nicobar and Andaman islands. Based on waveform comparison, we assert that the shallow portion of the megathrust offshore Banda Aceh had slip amplitudes of more than 20 m. Also, we find that significant amounts of slip (about 10 m) concentrated below the Andaman islands and did not propagate on the shallow portion of the interface. Although synthetic tests tend to show less resolution in the northern part of the rupture, this solution is compatible with the near-field data (GPS, coral heads and imagery), and would allow one to explain the apparent paradox between the large local displacements and the moderate tsunami observed locally. Finally, we demonstrate the rapidly dominating effect of propagation and slip distribution over the rupture velocity, and how it precludes the direct estimate of this latter parameter.