The authors thank professor Sj berg for having interest in our paper. The main goal of the paper is to test kernel modification methods used in geoid computations. Our tests found that Vanicek/Kleusberg's and Featherstone's methods fit the GPS/leveling data the best in the relative sense at various cap sizes. At the same time, we also pointed out that their methods are unstable and the mean values change from dm to meters by just changing the cap size. By contrast, the modification of the Wong and Gore type (including the spectral combination, method of Heck and Grüninger) is stable and insensitive to the truncation degree and cap size. This feature is especially useful when we know the accuracy of the gravity field at different frequency bands. For instance, it is advisable to truncate Stokes' kernel at a degree to which the satellite model is believed to be more accurate than surface data. The method of the Wong and Goretype does this job quite well. In contrast, the low degrees of Stokes' kernel are modified by Molodensky's coefficients tn in Vanicek/Kleusberg's and Featherstone's methods (cf. Eq. (6) in Li and Wang (2011)). It implies that the low degree gravity field of the reference model will be altered by less accurate surface data in the final geoid. This is also the cause of the larger variation in mean values of the geoid.