Existing wind speed algorithms for satellite altimeters have been developed from data in the range 0 to 20 m/s. At higher wind speeds the available algorithms diverge alarmingly. By comparing Geosat altimeter values of the radar cross section with model predictions of the surface winds during satellite overpasses of tropical cyclones, a wind speed algorithm valid for wind speeds between 20 and 40 m/s is developed. There is, however, considerable scatter in these data. An error analysis shows that this observed scatter is consistent with the accuracy to which the tropical cyclone wind fields can be inferred. An approximately linear dependence of the radar cross section on wind speed is, however, clearly evident within these data. At the lower limit of its applicability (U10=20 m/s), these data are consistent with the previously derived algorithms. At its upper limit (U10=40 m/s), mean squared slope values inferred from the radar cross section are consistent with the theoretical upper limit. ¿ American Geophysical Union 1993