Seasat and Geosat satellite altimeter measurements for the Greenland ice sheet (south of 72 degrees N latitude) show that surface elevations above 2000 meters increased at an average rate of only 1.5 +/- 0.5 centimeters per year from 1978 to 1988. In contrast, elevation changes varied regionally from -15 to +18 centimeters per year, seasonally by +/-15 centimeters, and interannually by +/-8 centimeters. The average growth rate is too small to determine if the Greenland ice sheet is undergoing a long-term change due to a warmer polar climate.