The SEASAT-1 radar altimeter data set acquired over both the Antarctic and Greenland continental ice sheets is analyzed to obtain corrected ranges to the ice surface. The radar altimeter functional response over the continental ice sheets is considerably more complex than over the oceans. Causal factors identified in this complicated response include sloping surfaces, undulating ice surfaces with characteristic wavelengths on the same spatial scale as the atlimeter beam-limited footprint, off-track reflections, and dynamic lag of the altimeter tracking circuit. Retracking methods using the altimeter return pulse waveforms give range corrections that are typically several meters. The entire set of SEASAT-1 altimetry over the continental ice sheets is being retracked by fitting a multi-parameter function to each waveform. Many waveforms have double ramps indicating near-normal reflections from two distinct portions of the ice surface within the altimeter beam. Two independent range measurements differing by less than 25 m are obtained from retracking the double-ramp waveforms.