In this paper, new rigorous, simpler, and more efficient formulas are used to estimate the effect of the terrain on geoid undulations and defections of the vertical. The new formulas are based on the successive application in the spectral domain of Molodensky's vertical derivative operator to powers of heights. A number of numerical tests are carried out in the area of British Columbia (BC) in western Canada. Geoid undulations and deflections of the vertical are computed by combining a geopotential model complete to degree and order 360, mean 5 arc min¿5 arc min free air gravity anomalies and height data on a 1 km¿1 km grid. In geoid undulation computations, the indirect effect of Helmert's second condensation reduction is taken into account. To assess the quality of the predicted deflections of the vertical and geoid undulations, the computed quantities are compared to a set of astronomic deflections of the vertical and geoid undulations derived from a combination of Global Positioning System with leveled orthometric heights. Test results present a precision of about ¿2.0 arc sec for deflections, thus fulfilling the requirements for the reduction of geodetic measurements in any case. The achievable precision for geoid undulation differences, close to ¿0.50 m, is also acceptable to determine an accurate relative geoid in the test are a useful for various geodetic applications. ¿ American Geophysical Union 1992