The Indian Ocean tsunami, which occurred on December 26, 2004, was the first to be clearly observed using satellite altimeters. The wave amplitude observed in deep-ocean by TOPEX and Jason-1 was close to 60 cm about 2 hours after the earthquake. Envisat crossed the tsunami wave 3h15 after the earthquake and measured a 35 cm wave. Even though it flew over the tsunami 7h20 after the earthquake, GFO still observed a wave close to 20 cm. To better extract the tsunami signal from altimeter measurements, a specific ocean variability mapping technique is used. This technique proves to be mandatory for discriminating tsunami waves from other ocean signals. Altimeter signals are then compared with those derived from the CEA (Commissariat à l'Energie Atomique) model outputs. For the first time with altimeter data, peculiar short wavelengths signals along Jason-1 and Envisat profiles have been detected from the analysis of 20-Hz altimeter measurements. Such high wavenumber signals can be explained by the dispersive propagation of tsunami waves. These observations highlight the essential role of satellite altimeter measurements to better understand and to improve models of tsunami wave propagation and dissipation.