Satellite radar altimetry has been an important tool for cryospheric applications such as measuring ice-sheet height or assessing anomalies in snow and ice properties (e.g. the extensive melt in Greenland in 2012). Although accurate height measurements are key for such applications, slope-induced errors due to undulating topography within the kilometre-wide beam-limited footprint can cause multi-metre errors. Two main correction methods that have been developed (referred to as the slope- and point-based methods) neglect either the actual topography or the actual footprint that can be estimated by a combination of the leading edge and topography. Therefore, a leading edge point-based (LEPTA) method is presented that corrects for the slope-induced error by including the leading edge information of the radar waveform to determine the impact point. The principle of the method is that only the points on the ground that are within the range determined by the beginning and end of the leading edge are used to determine the impact point. Benchmarking of the LEPTA method against the slope- and point-based methods based on CryoSat-2 Low Resolution Mode (LRM) acquisitions over Greenland in 2019 shows that, when compared to ICESat-2 observations, the LEPTA method has a stable performance both in the flat, interior regions of Greenland and in regions with more complex topography. The median difference between the slope-corrected CryoSat-2 heights using LEPTA and the ICESat-2 heights is at the millimetre level, whereas the slope and point-based methods can have a 0.21 and 0.48 m difference, respectively, and the Level-2I (L2I) data provided by ESA have a 0.01 m difference. The median absolute deviation of height differences between CryoSat-2 and ICESat-2, which we use as an indicator of the variation in errors, is also the lowest for LEPTA (0.09 m) in comparison to the aforementioned methods (0.19 m for slope method and 0.10 m for point-based method) and ESA Level-2 data (0.14 m). Although ESA Level-2 products and the point-based method have good performance in either the median or the median absolute deviation, LEPTA shows a good performance in both metrics. Based on that, we recommend considering LEPTA for obtaining accurate height measurements with radar altimetry data, especially towards the margins of the LRM coverage where the surface slopes increase.