Ranges obtained by radar altimetry from a satellite to a sloping surface ont he earth are not measurements of t he surface elevation at the subsatellite point. Instead, the reflecting point is displaced upslope from the subsatellite point causing a 'slope-induced error' between the true range to the subsatellite point and the indicated range. For the SEASAT 1 altimeter, this range error is nearly 80 m for a 0.8 degree slope. Ice sheet surface slopes are frequently large enough to cause errors of 10 m or more. In addition, undulations in the surface about a mean slope cause pronounced variations in these errors. Altimeter measurements of ranges to modeled irregular surfaces are simulated and two correction schemes are used to reconstruct the modeled surfaces from the simulated data. The results illustrate the fundamental limitations inherent in single-beam radar altimetry for mapping irregular surfaces. In the simpler two-dimensional case, for which cross-track slopes are neglected, a relocation scheme, which constructs a surface consistent with the altimeter ranges, removes 85% of the rms error. The mean error along profiles of about 75 km or longer is usually reduced more than the rms error. An alternate slope correction scheme, which uses the local slope ot calculate the expected error, is less effective in the two-dimensional case. However, over a simulated three-dimensional surface, where groundtracks are widely spaced and cross-track sloeps are significant, the slope-correction method must be used in at least the cross-track direction. The effectiveness of the three-dimensional correction depends on the relative size of the errors caused by the local slope on surface undulations in comparison to the regional slope.