Since the devastating earthquake and tsunami in 2004 offshore Sumatra, many source models have been put forward. Recent studies clearly show that modern GPS-processing could achieve high resolving power for slip in near real time, which is crucial for determining tsunami initial conditions, provided accurate GPS-processing and inversion. Here, we propose an inversion technique with improved representation of the subduction zone geometry and physically justified boundary conditions. We show that the discrepancy between the inversion of near- and far field GPS data for the 2004 event, which is often explained by postseismic slip, can be eliminated by using our inversion method and IASP91 earth model. Inverted source models, including versions with splay faulting, are shown to be consistent with satellite altimetry data of offshore tsunami wave height, suggesting that displacement at the splay fault might have been present but was likely a second order process.